7th Grade Math · Unit 2
Negative powers of 10. Swoop the decimal point to the left, and fill empty places with zeros.
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digit . stuff × 10 to the swoops
Draw a short line for the digit. Then a decimal point. Then a longer line for the other digits. Then × 10 to the number of swoops.
Negative exponents swoop left
The exponent is the number of swoops. Swoop the decimal point to the left that many times.
Fill each empty place with a zero.
The number is small and positive. A negative exponent does not make a negative number.
Back to scientific notation
A small number already shows its decimal point.
Swoop right until one digit is in front of the decimal point.
The number of swoops is the exponent, and the exponent is negative.
Negative powers of 10. Swoop left. Problems 1–10 have an integer coefficient. Problems 11–20 have a decimal coefficient.
7 × 10⁻²
The exponent is −2, so the decimal point makes 2 swoops to the left.
Write digit . stuff × 10 to the number of swoops.
The longer line is empty, so the coefficient is a whole number.
0.07
Answer: 0.07
6.2 × 10⁻⁴
The exponent is −4, so the decimal point makes 4 swoops to the left.
Write digit . stuff × 10 to the number of swoops.
0.00062
Answer: 0.00062
3 × 10⁻²
The exponent is −2, so the decimal point makes 2 swoops to the left.
Write digit . stuff × 10 to the number of swoops.
The longer line is empty, so the coefficient is a whole number.
0.03
Answer: 0.03
7 × 10⁻⁴
The exponent is −4, so the decimal point makes 4 swoops to the left.
Write digit . stuff × 10 to the number of swoops.
The longer line is empty, so the coefficient is a whole number.
0.0007
Answer: 0.0007
2 × 10⁻¹
The exponent is −1, so the decimal point makes 1 swoop to the left.
Write digit . stuff × 10 to the number of swoops.
The longer line is empty, so the coefficient is a whole number.
0.2
Answer: 0.2
9 × 10⁻³
The exponent is −3, so the decimal point makes 3 swoops to the left.
Write digit . stuff × 10 to the number of swoops.
The longer line is empty, so the coefficient is a whole number.
0.009
Answer: 0.009
5 × 10⁻⁵
The exponent is −5, so the decimal point makes 5 swoops to the left.
Write digit . stuff × 10 to the number of swoops.
The longer line is empty, so the coefficient is a whole number.
0.00005
Answer: 0.00005
8 × 10⁻²
The exponent is −2, so the decimal point makes 2 swoops to the left.
Write digit . stuff × 10 to the number of swoops.
The longer line is empty, so the coefficient is a whole number.
0.08
Answer: 0.08
1 × 10⁻³
The exponent is −3, so the decimal point makes 3 swoops to the left.
Write digit . stuff × 10 to the number of swoops.
The longer line is empty, so the coefficient is a whole number.
0.001
Answer: 0.001
6 × 10⁻⁶
The exponent is −6, so the decimal point makes 6 swoops to the left.
Write digit . stuff × 10 to the number of swoops.
The longer line is empty, so the coefficient is a whole number.
0.000006
Answer: 0.000006
4 × 10⁻⁴
The exponent is −4, so the decimal point makes 4 swoops to the left.
Write digit . stuff × 10 to the number of swoops.
The longer line is empty, so the coefficient is a whole number.
0.0004
Answer: 0.0004
3 × 10⁻⁵
The exponent is −5, so the decimal point makes 5 swoops to the left.
Write digit . stuff × 10 to the number of swoops.
The longer line is empty, so the coefficient is a whole number.
0.00003
Answer: 0.00003
2.5 × 10⁻²
The exponent is −2, so the decimal point makes 2 swoops to the left.
Write digit . stuff × 10 to the number of swoops.
0.025
Answer: 0.025
6.1 × 10⁻³
The exponent is −3, so the decimal point makes 3 swoops to the left.
Write digit . stuff × 10 to the number of swoops.
0.0061
Answer: 0.0061
8.4 × 10⁻¹
The exponent is −1, so the decimal point makes 1 swoop to the left.
Write digit . stuff × 10 to the number of swoops.
0.84
Answer: 0.84
1.7 × 10⁻⁴
The exponent is −4, so the decimal point makes 4 swoops to the left.
Write digit . stuff × 10 to the number of swoops.
0.00017
Answer: 0.00017
9.2 × 10⁻⁵
The exponent is −5, so the decimal point makes 5 swoops to the left.
Write digit . stuff × 10 to the number of swoops.
0.000092
Answer: 0.000092
3.05 × 10⁻³
The exponent is −3, so the decimal point makes 3 swoops to the left.
Write digit . stuff × 10 to the number of swoops.
0.00305
Answer: 0.00305
4.8 × 10⁻²
The exponent is −2, so the decimal point makes 2 swoops to the left.
Write digit . stuff × 10 to the number of swoops.
0.048
Answer: 0.048
7.6 × 10⁻⁶
The exponent is −6, so the decimal point makes 6 swoops to the left.
Write digit . stuff × 10 to the number of swoops.
0.0000076
Answer: 0.0000076
5.3 × 10⁻⁴
The exponent is −4, so the decimal point makes 4 swoops to the left.
Write digit . stuff × 10 to the number of swoops.
0.00053
Answer: 0.00053
1.09 × 10⁻³
The exponent is −3, so the decimal point makes 3 swoops to the left.
Write digit . stuff × 10 to the number of swoops.
0.00109
Answer: 0.00109
The decimal point is already written. Swoop right. The exponent is negative. Problems 1–10 have an integer coefficient. Problems 11–20 have a decimal coefficient.
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 3 swoops.
Write digit . stuff × 10 to the number of swoops.
The other digits are zeros, so the longer line stays empty.
8 × 10⁻³
Answer: 8 × 10⁻³
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 3 swoops.
Write digit . stuff × 10 to the number of swoops.
4.5 × 10⁻³
Answer: 4.5 × 10⁻³
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 2 swoops.
Write digit . stuff × 10 to the number of swoops.
The other digits are zeros, so the longer line stays empty.
5 × 10⁻²
Answer: 5 × 10⁻²
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 4 swoops.
Write digit . stuff × 10 to the number of swoops.
The other digits are zeros, so the longer line stays empty.
8 × 10⁻⁴
Answer: 8 × 10⁻⁴
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 1 swoop.
Write digit . stuff × 10 to the number of swoops.
The other digits are zeros, so the longer line stays empty.
3 × 10⁻¹
Answer: 3 × 10⁻¹
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 5 swoops.
Write digit . stuff × 10 to the number of swoops.
The other digits are zeros, so the longer line stays empty.
4 × 10⁻⁵
Answer: 4 × 10⁻⁵
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 3 swoops.
Write digit . stuff × 10 to the number of swoops.
The other digits are zeros, so the longer line stays empty.
7 × 10⁻³
Answer: 7 × 10⁻³
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 6 swoops.
Write digit . stuff × 10 to the number of swoops.
The other digits are zeros, so the longer line stays empty.
9 × 10⁻⁶
Answer: 9 × 10⁻⁶
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 2 swoops.
Write digit . stuff × 10 to the number of swoops.
The other digits are zeros, so the longer line stays empty.
2 × 10⁻²
Answer: 2 × 10⁻²
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 4 swoops.
Write digit . stuff × 10 to the number of swoops.
The other digits are zeros, so the longer line stays empty.
1 × 10⁻⁴
Answer: 1 × 10⁻⁴
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 1 swoop.
Write digit . stuff × 10 to the number of swoops.
The other digits are zeros, so the longer line stays empty.
6 × 10⁻¹
Answer: 6 × 10⁻¹
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 6 swoops.
Write digit . stuff × 10 to the number of swoops.
The other digits are zeros, so the longer line stays empty.
3 × 10⁻⁶
Answer: 3 × 10⁻⁶
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 2 swoops.
Write digit . stuff × 10 to the number of swoops.
4.7 × 10⁻²
Answer: 4.7 × 10⁻²
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 3 swoops.
Write digit . stuff × 10 to the number of swoops.
3.8 × 10⁻³
Answer: 3.8 × 10⁻³
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 1 swoop.
Write digit . stuff × 10 to the number of swoops.
9.1 × 10⁻¹
Answer: 9.1 × 10⁻¹
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 4 swoops.
Write digit . stuff × 10 to the number of swoops.
2.5 × 10⁻⁴
Answer: 2.5 × 10⁻⁴
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 5 swoops.
Write digit . stuff × 10 to the number of swoops.
6.2 × 10⁻⁵
Answer: 6.2 × 10⁻⁵
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 2 swoops.
Write digit . stuff × 10 to the number of swoops.
1.04 × 10⁻²
Answer: 1.04 × 10⁻²
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 3 swoops.
Write digit . stuff × 10 to the number of swoops.
5.7 × 10⁻³
Answer: 5.7 × 10⁻³
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 6 swoops.
Write digit . stuff × 10 to the number of swoops.
8.3 × 10⁻⁶
Answer: 8.3 × 10⁻⁶
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 1 swoop.
Write digit . stuff × 10 to the number of swoops.
4.6 × 10⁻¹
Answer: 4.6 × 10⁻¹
The decimal point is already written in the number.
Swoop the decimal point right until one digit is in front of it. That is 4 swoops.
Write digit . stuff × 10 to the number of swoops.
7.09 × 10⁻⁴
Answer: 7.09 × 10⁻⁴
Write the standard form, then count the zeros between the decimal point and the first nonzero digit.
Write the standard form first. The exponent is the number of swoops.
3 × 10⁻⁴
The exponent is −4, so the decimal point makes 4 swoops to the left.
3 → 0.0003
The zeros between the decimal point and 3: 3.
Answer: 3
Write the standard form first. The exponent is the number of swoops.
4 × 10⁻⁵
The exponent is −5, so the decimal point makes 5 swoops to the left.
4 → 0.00004
The zeros between the decimal point and 4: 4.
Answer: 4
Write the standard form first. The exponent is the number of swoops.
9 × 10⁻²
The exponent is −2, so the decimal point makes 2 swoops to the left.
9 → 0.09
The zeros between the decimal point and 9: 1.
Answer: 1
Write the standard form first. The exponent is the number of swoops.
6 × 10⁻⁷
The exponent is −7, so the decimal point makes 7 swoops to the left.
6 → 0.0000006
The zeros between the decimal point and 6: 6.
Answer: 6
Write the standard form first. The exponent is the number of swoops.
5.2 × 10⁻³
The exponent is −3, so the decimal point makes 3 swoops to the left.
5.2 → 0.0052
The zeros between the decimal point and 5: 2.
Answer: 2
Write the standard form first. The exponent is the number of swoops.
1.08 × 10⁻⁴
The exponent is −4, so the decimal point makes 4 swoops to the left.
1.08 → 0.000108
The zeros between the decimal point and 1: 3.
Answer: 3
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