M
Math Coach Amy
Amy Ferguson Moncure

7th Grade Math · Unit 2

Compare Numbers in
Scientific Notation

Put up to four numbers written in scientific notation in order.

Jump to section:

What to Remember

Compare the exponents first

For numbers greater than 0, the greater power of 10 is the greater number.

2 × 10⁵ is greater than 9 × 10³ because 5 > 3.

Same exponent, compare the front

If the powers of 10 match, compare the coefficients.

7.1 × 10⁻¹ > 6.9 × 10⁻¹ because 7.1 > 6.9.

A negative exponent is a small positive

4 × 10⁻³ = 0.004. It is greater than 0 and less than 1.

It is much smaller than 4 × 10³ = 4,000.

Order up to four

Line the numbers up by exponent. Break ties with the coefficient.

Least to greatest uses <. Greatest to least uses >. The same value uses =.

Level 1

Easy

Compare two numbers.

Example
Compare. Write <, >, or =.
3 × 10⁴    ?    3 × 10²

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

3 × 10⁴ has exponent 4 and coefficient 3.

3 × 10² has exponent 2 and coefficient 3.

The exponents are different, so 3 × 10⁴ is greater.

The coefficient does not decide this one. The exponent does.

3 × 10⁴ > 3 × 10²

Answer: 3 × 10⁴ > 3 × 10²

1
Compare. Write <, >, or =.
2 × 10³    ?    2 × 10⁵
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

2 × 10³ has exponent 3 and coefficient 2.

2 × 10⁵ has exponent 5 and coefficient 2.

The exponents are different, so 2 × 10⁵ is greater.

2 × 10³ < 2 × 10⁵

Answer: 2 × 10³ < 2 × 10⁵

2
Compare. Write <, >, or =.
7 × 10²    ?    9 × 10⁴
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

7 × 10² has exponent 2 and coefficient 7.

9 × 10⁴ has exponent 4 and coefficient 9.

The exponents are different, so 9 × 10⁴ is greater.

7 × 10² < 9 × 10⁴

Answer: 7 × 10² < 9 × 10⁴

3
Compare. Write <, >, or =.
4 × 10⁻¹    ?    4 × 10⁻³
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

4 × 10⁻¹ has exponent −1 and coefficient 4.

4 × 10⁻³ has exponent −3 and coefficient 4.

The exponents are different, so 4 × 10⁻¹ is greater.

The coefficient does not decide this one. The exponent does.

4 × 10⁻¹ > 4 × 10⁻³

Answer: 4 × 10⁻¹ > 4 × 10⁻³

4
Compare. Write <, >, or =.
6 × 10⁻²    ?    1 × 10¹
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

6 × 10⁻² has exponent −2 and coefficient 6.

1 × 10¹ has exponent 1 and coefficient 1.

The exponents are different, so 1 × 10¹ is greater.

The coefficient does not decide this one. The exponent does.

6 × 10⁻² < 1 × 10¹

Answer: 6 × 10⁻² < 1 × 10¹

5
Compare. Write <, >, or =.
8 × 10³    ?    8 × 10³
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

8 × 10³ has exponent 3 and coefficient 8.

8 × 10³ has exponent 3 and coefficient 8.

The exponents match, so the coefficients decide.

8 × 10³ = 8 × 10³

Answer: 8 × 10³ = 8 × 10³

6
Compare. Write <, >, or =.
1.2 × 10³    ?    9.9 × 10²
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

1.2 × 10³ has exponent 3 and coefficient 1.2.

9.9 × 10² has exponent 2 and coefficient 9.9.

The exponents are different, so 1.2 × 10³ is greater.

The coefficient does not decide this one. The exponent does.

1.2 × 10³ > 9.9 × 10²

Answer: 1.2 × 10³ > 9.9 × 10²

7
Compare. Write <, >, or =.
5 × 10⁶    ?    5 × 10⁴
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

5 × 10⁶ has exponent 6 and coefficient 5.

5 × 10⁴ has exponent 4 and coefficient 5.

The exponents are different, so 5 × 10⁶ is greater.

The coefficient does not decide this one. The exponent does.

5 × 10⁶ > 5 × 10⁴

Answer: 5 × 10⁶ > 5 × 10⁴

8
Compare. Write <, >, or =.
3 × 10⁻⁴    ?    3 × 10⁻²
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

3 × 10⁻⁴ has exponent −4 and coefficient 3.

3 × 10⁻² has exponent −2 and coefficient 3.

The exponents are different, so 3 × 10⁻² is greater.

3 × 10⁻⁴ < 3 × 10⁻²

Answer: 3 × 10⁻⁴ < 3 × 10⁻²

9
Compare. Write <, >, or =.
9 × 10¹    ?    1 × 10²
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

9 × 10¹ has exponent 1 and coefficient 9.

1 × 10² has exponent 2 and coefficient 1.

The exponents are different, so 1 × 10² is greater.

The coefficient does not decide this one. The exponent does.

9 × 10¹ < 1 × 10²

Answer: 9 × 10¹ < 1 × 10²

10
Compare. Write <, >, or =.
7.1 × 10⁻¹    ?    6.9 × 10⁻¹
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

7.1 × 10⁻¹ has exponent −1 and coefficient 7.1.

6.9 × 10⁻¹ has exponent −1 and coefficient 6.9.

The exponents match, so the coefficients decide.

7.1 × 10⁻¹ > 6.9 × 10⁻¹

Answer: 7.1 × 10⁻¹ > 6.9 × 10⁻¹

Level 2

Medium

Order three numbers.

Example
Order from least to greatest.
2 × 10³  2 × 10²  2 × 10⁴

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

2 × 10³ has exponent 3 and coefficient 2.

2 × 10² has exponent 2 and coefficient 2.

2 × 10⁴ has exponent 4 and coefficient 2.

Least to greatest:

2 × 10² < 2 × 10³ < 2 × 10⁴

Answer: 2 × 10² < 2 × 10³ < 2 × 10⁴

1
Order from least to greatest.
4 × 10²  4 × 10⁵  4 × 10³
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

4 × 10² has exponent 2 and coefficient 4.

4 × 10⁵ has exponent 5 and coefficient 4.

4 × 10³ has exponent 3 and coefficient 4.

Least to greatest:

4 × 10² < 4 × 10³ < 4 × 10⁵

Answer: 4 × 10² < 4 × 10³ < 4 × 10⁵

2
Order from least to greatest.
1 × 10⁻¹  1 × 10⁻³  1 × 10⁻²
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

1 × 10⁻¹ has exponent −1 and coefficient 1.

1 × 10⁻³ has exponent −3 and coefficient 1.

1 × 10⁻² has exponent −2 and coefficient 1.

Least to greatest:

1 × 10⁻³ < 1 × 10⁻² < 1 × 10⁻¹

Answer: 1 × 10⁻³ < 1 × 10⁻² < 1 × 10⁻¹

3
Order from least to greatest.
6 × 10³  8 × 10³  2 × 10³
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

6 × 10³ has exponent 3 and coefficient 6.

8 × 10³ has exponent 3 and coefficient 8.

2 × 10³ has exponent 3 and coefficient 2.

Least to greatest:

2 × 10³ < 6 × 10³ < 8 × 10³

Answer: 2 × 10³ < 6 × 10³ < 8 × 10³

4
Order from least to greatest.
9 × 10²  1.1 × 10³  9.5 × 10²
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

9 × 10² has exponent 2 and coefficient 9.

1.1 × 10³ has exponent 3 and coefficient 1.1.

9.5 × 10² has exponent 2 and coefficient 9.5.

Least to greatest:

9 × 10² < 9.5 × 10² < 1.1 × 10³

Answer: 9 × 10² < 9.5 × 10² < 1.1 × 10³

5
Order from least to greatest.
3 × 10⁻²  3 × 10⁻⁴  5 × 10⁻³
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

3 × 10⁻² has exponent −2 and coefficient 3.

3 × 10⁻⁴ has exponent −4 and coefficient 3.

5 × 10⁻³ has exponent −3 and coefficient 5.

Least to greatest:

3 × 10⁻⁴ < 5 × 10⁻³ < 3 × 10⁻²

Answer: 3 × 10⁻⁴ < 5 × 10⁻³ < 3 × 10⁻²

6
Order from least to greatest.
7.2 × 10⁴  7.20 × 10⁴  7.1 × 10⁴
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

7.2 × 10⁴ has exponent 4 and coefficient 7.2.

7.20 × 10⁴ has exponent 4 and coefficient 7.20.

7.1 × 10⁴ has exponent 4 and coefficient 7.1.

Least to greatest:

7.1 × 10⁴ < 7.2 × 10⁴ = 7.20 × 10⁴

Answer: 7.1 × 10⁴ < 7.2 × 10⁴ = 7.20 × 10⁴

7
Order from greatest to least.
2 × 10⁵  8 × 10⁴  3 × 10⁶
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

2 × 10⁵ has exponent 5 and coefficient 2.

8 × 10⁴ has exponent 4 and coefficient 8.

3 × 10⁶ has exponent 6 and coefficient 3.

Greatest to least:

3 × 10⁶ > 2 × 10⁵ > 8 × 10⁴

Answer: 3 × 10⁶ > 2 × 10⁵ > 8 × 10⁴

8
Order from least to greatest.
4.5 × 10⁻¹  4.5 × 10⁻³  9 × 10⁻²
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

4.5 × 10⁻¹ has exponent −1 and coefficient 4.5.

4.5 × 10⁻³ has exponent −3 and coefficient 4.5.

9 × 10⁻² has exponent −2 and coefficient 9.

Least to greatest:

4.5 × 10⁻³ < 9 × 10⁻² < 4.5 × 10⁻¹

Answer: 4.5 × 10⁻³ < 9 × 10⁻² < 4.5 × 10⁻¹

9
Order from least to greatest.
1.05 × 10²  9.9 × 10¹  1 × 10²
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

1.05 × 10² has exponent 2 and coefficient 1.05.

9.9 × 10¹ has exponent 1 and coefficient 9.9.

1 × 10² has exponent 2 and coefficient 1.

Least to greatest:

9.9 × 10¹ < 1 × 10² < 1.05 × 10²

Answer: 9.9 × 10¹ < 1 × 10² < 1.05 × 10²

10
Order from least to greatest.
6 × 10⁻⁵  6 × 10⁻³  6 × 10⁻⁴
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

6 × 10⁻⁵ has exponent −5 and coefficient 6.

6 × 10⁻³ has exponent −3 and coefficient 6.

6 × 10⁻⁴ has exponent −4 and coefficient 6.

Least to greatest:

6 × 10⁻⁵ < 6 × 10⁻⁴ < 6 × 10⁻³

Answer: 6 × 10⁻⁵ < 6 × 10⁻⁴ < 6 × 10⁻³

Level 3

Hard

Order four numbers.

Example
Order from least to greatest.
3.2 × 10⁴3.2 × 10³9.1 × 10³4 × 10⁴

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

3.2 × 10⁴ has exponent 4 and coefficient 3.2.

3.2 × 10³ has exponent 3 and coefficient 3.2.

9.1 × 10³ has exponent 3 and coefficient 9.1.

4 × 10⁴ has exponent 4 and coefficient 4.

Least to greatest:

3.2 × 10³ < 9.1 × 10³ < 3.2 × 10⁴ < 4 × 10⁴

Answer: 3.2 × 10³ < 9.1 × 10³ < 3.2 × 10⁴ < 4 × 10⁴

1
Order from least to greatest.
2 × 10³1.9 × 10³2.1 × 10⁴9 × 10²
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

2 × 10³ has exponent 3 and coefficient 2.

1.9 × 10³ has exponent 3 and coefficient 1.9.

2.1 × 10⁴ has exponent 4 and coefficient 2.1.

9 × 10² has exponent 2 and coefficient 9.

Least to greatest:

9 × 10² < 1.9 × 10³ < 2 × 10³ < 2.1 × 10⁴

Answer: 9 × 10² < 1.9 × 10³ < 2 × 10³ < 2.1 × 10⁴

2
Order from least to greatest.
5 × 10⁻²5 × 10⁻³4.8 × 10⁻²6 × 10⁻¹
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

5 × 10⁻² has exponent −2 and coefficient 5.

5 × 10⁻³ has exponent −3 and coefficient 5.

4.8 × 10⁻² has exponent −2 and coefficient 4.8.

6 × 10⁻¹ has exponent −1 and coefficient 6.

Least to greatest:

5 × 10⁻³ < 4.8 × 10⁻² < 5 × 10⁻² < 6 × 10⁻¹

Answer: 5 × 10⁻³ < 4.8 × 10⁻² < 5 × 10⁻² < 6 × 10⁻¹

3
Order from greatest to least.
7.5 × 10⁶8 × 10⁵7.5 × 10⁵1.2 × 10⁶
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

7.5 × 10⁶ has exponent 6 and coefficient 7.5.

8 × 10⁵ has exponent 5 and coefficient 8.

7.5 × 10⁵ has exponent 5 and coefficient 7.5.

1.2 × 10⁶ has exponent 6 and coefficient 1.2.

Greatest to least:

7.5 × 10⁶ > 1.2 × 10⁶ > 8 × 10⁵ > 7.5 × 10⁵

Answer: 7.5 × 10⁶ > 1.2 × 10⁶ > 8 × 10⁵ > 7.5 × 10⁵

4
Order from least to greatest.
3 × 10⁴3.01 × 10⁴2.99 × 10⁴3 × 10³
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

3 × 10⁴ has exponent 4 and coefficient 3.

3.01 × 10⁴ has exponent 4 and coefficient 3.01.

2.99 × 10⁴ has exponent 4 and coefficient 2.99.

3 × 10³ has exponent 3 and coefficient 3.

Least to greatest:

3 × 10³ < 2.99 × 10⁴ < 3 × 10⁴ < 3.01 × 10⁴

Answer: 3 × 10³ < 2.99 × 10⁴ < 3 × 10⁴ < 3.01 × 10⁴

5
Order from least to greatest.
1.4 × 10⁻³1.4 × 10⁻⁴9.9 × 10⁻⁴2 × 10⁻³
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

1.4 × 10⁻³ has exponent −3 and coefficient 1.4.

1.4 × 10⁻⁴ has exponent −4 and coefficient 1.4.

9.9 × 10⁻⁴ has exponent −4 and coefficient 9.9.

2 × 10⁻³ has exponent −3 and coefficient 2.

Least to greatest:

1.4 × 10⁻⁴ < 9.9 × 10⁻⁴ < 1.4 × 10⁻³ < 2 × 10⁻³

Answer: 1.4 × 10⁻⁴ < 9.9 × 10⁻⁴ < 1.4 × 10⁻³ < 2 × 10⁻³

6
Order from least to greatest.
6.2 × 10³6.20 × 10³6.02 × 10³6.2 × 10⁴
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

6.2 × 10³ has exponent 3 and coefficient 6.2.

6.20 × 10³ has exponent 3 and coefficient 6.20.

6.02 × 10³ has exponent 3 and coefficient 6.02.

6.2 × 10⁴ has exponent 4 and coefficient 6.2.

Least to greatest:

6.02 × 10³ < 6.2 × 10³ = 6.20 × 10³ < 6.2 × 10⁴

Answer: 6.02 × 10³ < 6.2 × 10³ = 6.20 × 10³ < 6.2 × 10⁴

7
Order from greatest to least.
9 × 10⁻¹1.1 × 10⁰9.9 × 10⁻¹8 × 10⁻¹
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

9 × 10⁻¹ has exponent −1 and coefficient 9.

1.1 × 10⁰ has exponent 0 and coefficient 1.1.

9.9 × 10⁻¹ has exponent −1 and coefficient 9.9.

8 × 10⁻¹ has exponent −1 and coefficient 8.

Greatest to least:

1.1 × 10⁰ > 9.9 × 10⁻¹ > 9 × 10⁻¹ > 8 × 10⁻¹

Answer: 1.1 × 10⁰ > 9.9 × 10⁻¹ > 9 × 10⁻¹ > 8 × 10⁻¹

8
Order from least to greatest.
2.5 × 10²2.5 × 10³2.05 × 10³3 × 10²
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

2.5 × 10² has exponent 2 and coefficient 2.5.

2.5 × 10³ has exponent 3 and coefficient 2.5.

2.05 × 10³ has exponent 3 and coefficient 2.05.

3 × 10² has exponent 2 and coefficient 3.

Least to greatest:

2.5 × 10² < 3 × 10² < 2.05 × 10³ < 2.5 × 10³

Answer: 2.5 × 10² < 3 × 10² < 2.05 × 10³ < 2.5 × 10³

9
Order from least to greatest.
8.4 × 10⁻⁴8.4 × 10⁻²1.2 × 10⁻³9 × 10⁻⁴
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

8.4 × 10⁻⁴ has exponent −4 and coefficient 8.4.

8.4 × 10⁻² has exponent −2 and coefficient 8.4.

1.2 × 10⁻³ has exponent −3 and coefficient 1.2.

9 × 10⁻⁴ has exponent −4 and coefficient 9.

Least to greatest:

8.4 × 10⁻⁴ < 9 × 10⁻⁴ < 1.2 × 10⁻³ < 8.4 × 10⁻²

Answer: 8.4 × 10⁻⁴ < 9 × 10⁻⁴ < 1.2 × 10⁻³ < 8.4 × 10⁻²

10
Order from greatest to least.
1 × 10⁴9.99 × 10³1.01 × 10⁴1 × 10⁵
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

1 × 10⁴ has exponent 4 and coefficient 1.

9.99 × 10³ has exponent 3 and coefficient 9.99.

1.01 × 10⁴ has exponent 4 and coefficient 1.01.

1 × 10⁵ has exponent 5 and coefficient 1.

Greatest to least:

1 × 10⁵ > 1.01 × 10⁴ > 1 × 10⁴ > 9.99 × 10³

Answer: 1 × 10⁵ > 1.01 × 10⁴ > 1 × 10⁴ > 9.99 × 10³

Extra

Ascending and Descending

Descending means greatest to least. Ascending means least to greatest. Compare exponents first.

Example
Place these numbers in descending order (greatest to least).
1.5 × 10⁻²  9 × 10⁻⁴  3.3 × 10⁻³  6 × 10⁻⁵

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

1.5 × 10⁻² has exponent −2 and coefficient 1.5.

9 × 10⁻⁴ has exponent −4 and coefficient 9.

3.3 × 10⁻³ has exponent −3 and coefficient 3.3.

6 × 10⁻⁵ has exponent −5 and coefficient 6.

Greatest to least:

1.5 × 10⁻² > 3.3 × 10⁻³ > 9 × 10⁻⁴ > 6 × 10⁻⁵

Answer: 1.5 × 10⁻² > 3.3 × 10⁻³ > 9 × 10⁻⁴ > 6 × 10⁻⁵

1
Place these numbers in descending order (greatest to least).
3.4 × 10⁻²  8 × 10⁻⁵  1.2 × 10⁻³  6.5 × 10⁻⁴
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

3.4 × 10⁻² has exponent −2 and coefficient 3.4.

8 × 10⁻⁵ has exponent −5 and coefficient 8.

1.2 × 10⁻³ has exponent −3 and coefficient 1.2.

6.5 × 10⁻⁴ has exponent −4 and coefficient 6.5.

Greatest to least:

3.4 × 10⁻² > 1.2 × 10⁻³ > 6.5 × 10⁻⁴ > 8 × 10⁻⁵

Answer: 3.4 × 10⁻² > 1.2 × 10⁻³ > 6.5 × 10⁻⁴ > 8 × 10⁻⁵

2
Place these numbers in descending order (greatest to least).
9.1 × 10⁻¹  4.4 × 10⁻⁴  2.2 × 10⁻²  7 × 10⁻³
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

9.1 × 10⁻¹ has exponent −1 and coefficient 9.1.

4.4 × 10⁻⁴ has exponent −4 and coefficient 4.4.

2.2 × 10⁻² has exponent −2 and coefficient 2.2.

7 × 10⁻³ has exponent −3 and coefficient 7.

Greatest to least:

9.1 × 10⁻¹ > 2.2 × 10⁻² > 7 × 10⁻³ > 4.4 × 10⁻⁴

Answer: 9.1 × 10⁻¹ > 2.2 × 10⁻² > 7 × 10⁻³ > 4.4 × 10⁻⁴

3
Place these numbers in descending order (greatest to least).
5 × 10⁻⁶  5 × 10⁻³  5.5 × 10⁻⁴  1.9 × 10⁻⁵
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

5 × 10⁻⁶ has exponent −6 and coefficient 5.

5 × 10⁻³ has exponent −3 and coefficient 5.

5.5 × 10⁻⁴ has exponent −4 and coefficient 5.5.

1.9 × 10⁻⁵ has exponent −5 and coefficient 1.9.

Greatest to least:

5 × 10⁻³ > 5.5 × 10⁻⁴ > 1.9 × 10⁻⁵ > 5 × 10⁻⁶

Answer: 5 × 10⁻³ > 5.5 × 10⁻⁴ > 1.9 × 10⁻⁵ > 5 × 10⁻⁶

4
Place these numbers in descending order (greatest to least).
6.08 × 10⁻²  6.8 × 10⁻³  9.9 × 10⁻⁴  1.04 × 10⁻²
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

6.08 × 10⁻² has exponent −2 and coefficient 6.08.

6.8 × 10⁻³ has exponent −3 and coefficient 6.8.

9.9 × 10⁻⁴ has exponent −4 and coefficient 9.9.

1.04 × 10⁻² has exponent −2 and coefficient 1.04.

Greatest to least:

6.08 × 10⁻² > 1.04 × 10⁻² > 6.8 × 10⁻³ > 9.9 × 10⁻⁴

Answer: 6.08 × 10⁻² > 1.04 × 10⁻² > 6.8 × 10⁻³ > 9.9 × 10⁻⁴

5
Place these numbers in descending order (greatest to least).
2.7 × 10⁻⁴  8.3 × 10⁻²  4 × 10⁻⁵  8.03 × 10⁻³
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

2.7 × 10⁻⁴ has exponent −4 and coefficient 2.7.

8.3 × 10⁻² has exponent −2 and coefficient 8.3.

4 × 10⁻⁵ has exponent −5 and coefficient 4.

8.03 × 10⁻³ has exponent −3 and coefficient 8.03.

Greatest to least:

8.3 × 10⁻² > 8.03 × 10⁻³ > 2.7 × 10⁻⁴ > 4 × 10⁻⁵

Answer: 8.3 × 10⁻² > 8.03 × 10⁻³ > 2.7 × 10⁻⁴ > 4 × 10⁻⁵

6
Place these numbers in ascending order (least to greatest).
4.2 × 10³  4.2 × 10⁻³  4.02 × 10²  4.002 × 10⁻¹
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

4.2 × 10³ has exponent 3 and coefficient 4.2.

4.2 × 10⁻³ has exponent −3 and coefficient 4.2.

4.02 × 10² has exponent 2 and coefficient 4.02.

4.002 × 10⁻¹ has exponent −1 and coefficient 4.002.

Least to greatest:

4.2 × 10⁻³ < 4.002 × 10⁻¹ < 4.02 × 10² < 4.2 × 10³

Answer: 4.2 × 10⁻³ < 4.002 × 10⁻¹ < 4.02 × 10² < 4.2 × 10³

7
Place these numbers in ascending order (least to greatest).
8.5 × 10⁴  8.5 × 10⁻²  8.05 × 10³  8.005 × 10⁰
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

8.5 × 10⁴ has exponent 4 and coefficient 8.5.

8.5 × 10⁻² has exponent −2 and coefficient 8.5.

8.05 × 10³ has exponent 3 and coefficient 8.05.

8.005 × 10⁰ has exponent 0 and coefficient 8.005.

Least to greatest:

8.5 × 10⁻² < 8.005 × 10⁰ < 8.05 × 10³ < 8.5 × 10⁴

Answer: 8.5 × 10⁻² < 8.005 × 10⁰ < 8.05 × 10³ < 8.5 × 10⁴

8
Place these numbers in ascending order (least to greatest).
1.6 × 10²  1.6 × 10⁻⁴  1.06 × 10¹  1.006 × 10⁻¹
Show Answer

For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

1.6 × 10² has exponent 2 and coefficient 1.6.

1.6 × 10⁻⁴ has exponent −4 and coefficient 1.6.

1.06 × 10¹ has exponent 1 and coefficient 1.06.

1.006 × 10⁻¹ has exponent −1 and coefficient 1.006.

Least to greatest:

1.6 × 10⁻⁴ < 1.006 × 10⁻¹ < 1.06 × 10¹ < 1.6 × 10²

Answer: 1.6 × 10⁻⁴ < 1.006 × 10⁻¹ < 1.06 × 10¹ < 1.6 × 10²

9
Place these numbers in ascending order (least to greatest).
3.9 × 10⁵  3.9 × 10⁻¹  3.09 × 10⁴  3.009 × 10²
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For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

3.9 × 10⁵ has exponent 5 and coefficient 3.9.

3.9 × 10⁻¹ has exponent −1 and coefficient 3.9.

3.09 × 10⁴ has exponent 4 and coefficient 3.09.

3.009 × 10² has exponent 2 and coefficient 3.009.

Least to greatest:

3.9 × 10⁻¹ < 3.009 × 10² < 3.09 × 10⁴ < 3.9 × 10⁵

Answer: 3.9 × 10⁻¹ < 3.009 × 10² < 3.09 × 10⁴ < 3.9 × 10⁵

10
Place these numbers in ascending order (least to greatest).
6.4 × 10⁻²  6.4 × 10³  6.04 × 10¹  6.004 × 10⁻³
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For a number greater than 0, the greater power of 10 is the greater number.

If the powers of 10 match, compare the coefficients.

6.4 × 10⁻² has exponent −2 and coefficient 6.4.

6.4 × 10³ has exponent 3 and coefficient 6.4.

6.04 × 10¹ has exponent 1 and coefficient 6.04.

6.004 × 10⁻³ has exponent −3 and coefficient 6.004.

Least to greatest:

6.004 × 10⁻³ < 6.4 × 10⁻² < 6.04 × 10¹ < 6.4 × 10³

Answer: 6.004 × 10⁻³ < 6.4 × 10⁻² < 6.04 × 10¹ < 6.4 × 10³

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