7th Grade Math · Unit 2
Positive and negative powers of 10. Choose which way the decimal point swoops.
Jump to section:
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.
Which way to swoop
A positive exponent swoops to the right. A negative exponent swoops to the left.
Going back to scientific notation, a large number swoops left and a small number swoops right.
Where the decimal starts
A whole number has an implied decimal at the end.
A small number already shows its decimal point.
Positive and negative powers. Problems 1–10 have an integer coefficient. Problems 11–20 have a decimal coefficient.
2.5 × 10⁴
The exponent is 4, so the decimal point makes 4 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
25,000
Answer: 25,000
3 × 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.
0.003
Answer: 0.003
7 × 10⁴
The exponent is 4, so the decimal point makes 4 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
The longer line is empty, so the coefficient is a whole number.
70,000
Answer: 70,000
6 × 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.
0.006
Answer: 0.006
2 × 10⁵
The exponent is 5, so the decimal point makes 5 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
The longer line is empty, so the coefficient is a whole number.
200,000
Answer: 200,000
9 × 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.
0.09
Answer: 0.09
4 × 10⁶
The exponent is 6, so the decimal point makes 6 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
The longer line is empty, so the coefficient is a whole number.
4,000,000
Answer: 4,000,000
8 × 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.
0.00008
Answer: 0.00008
1 × 10⁶
The exponent is 6, so the decimal point makes 6 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
The longer line is empty, so the coefficient is a whole number.
1,000,000
Answer: 1,000,000
5 × 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.
0.5
Answer: 0.5
3 × 10²
The exponent is 2, so the decimal point makes 2 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
The longer line is empty, so the coefficient is a whole number.
300
Answer: 300
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.
The longer line is empty, so the coefficient is a whole number.
0.0002
Answer: 0.0002
4.2 × 10³
The exponent is 3, so the decimal point makes 3 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
4,200
Answer: 4,200
7.5 × 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.
0.075
Answer: 0.075
1.8 × 10⁵
The exponent is 5, so the decimal point makes 5 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
180,000
Answer: 180,000
3.6 × 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.
0.00036
Answer: 0.00036
9.1 × 10²
The exponent is 2, so the decimal point makes 2 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
910
Answer: 910
2.04 × 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.
0.00204
Answer: 0.00204
6.7 × 10⁴
The exponent is 4, so the decimal point makes 4 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
67,000
Answer: 67,000
8.3 × 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.
0.83
Answer: 0.83
5.05 × 10⁶
The exponent is 6, so the decimal point makes 6 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
5,050,000
Answer: 5,050,000
1.4 × 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.
0.000014
Answer: 0.000014
Large numbers swoop left. Small numbers swoop right. Problems 1–10 have an integer coefficient. Problems 11–20 have a decimal coefficient.
4,500 has an implied decimal at the end of the number.
Swoop the decimal point left until one digit is in front of it. That is 3 swoops.
Write digit . stuff × 10 to the number of swoops.
Zeros at the end of the decimal do not go on the longer line.
4.5 × 10³
Answer: 4.5 × 10³
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.
7.2 × 10⁻³
Answer: 7.2 × 10⁻³
8,000 has an implied decimal at the end of the number.
Swoop the decimal point left 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 × 10³
Answer: 8 × 10³
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.
4 × 10⁻³
Answer: 4 × 10⁻³
500,000 has an implied decimal at the end of the number.
Swoop the decimal point left 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.
5 × 10⁵
Answer: 5 × 10⁵
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.
3 × 10⁻²
Answer: 3 × 10⁻²
600 has an implied decimal at the end of the number.
Swoop the decimal point left 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.
6 × 10²
Answer: 6 × 10²
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.
7 × 10⁻⁵
Answer: 7 × 10⁻⁵
2,000,000 has an implied decimal at the end of the number.
Swoop the decimal point left 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.
2 × 10⁶
Answer: 2 × 10⁶
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.
4 × 10⁻¹
Answer: 4 × 10⁻¹
90,000 has an implied decimal at the end of the number.
Swoop the decimal point left 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.
9 × 10⁴
Answer: 9 × 10⁴
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.
5 × 10⁻⁴
Answer: 5 × 10⁻⁴
4,700 has an implied decimal at the end of the number.
Swoop the decimal point left until one digit is in front of it. That is 3 swoops.
Write digit . stuff × 10 to the number of swoops.
Zeros at the end of the decimal do not go on the longer line.
4.7 × 10³
Answer: 4.7 × 10³
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.
8.2 × 10⁻²
Answer: 8.2 × 10⁻²
360,000 has an implied decimal at the end of the number.
Swoop the decimal point left until one digit is in front of it. That is 5 swoops.
Write digit . stuff × 10 to the number of swoops.
Zeros at the end of the decimal do not go on the longer line.
3.6 × 10⁵
Answer: 3.6 × 10⁵
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.
1.9 × 10⁻⁴
Answer: 1.9 × 10⁻⁴
2,050 has an implied decimal at the end of the number.
Swoop the decimal point left until one digit is in front of it. That is 3 swoops.
Write digit . stuff × 10 to the number of swoops.
Zeros at the end of the decimal do not go on the longer line.
2.05 × 10³
Answer: 2.05 × 10³
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.
6.4 × 10⁻³
Answer: 6.4 × 10⁻³
81,000 has an implied decimal at the end of the number.
Swoop the decimal point left until one digit is in front of it. That is 4 swoops.
Write digit . stuff × 10 to the number of swoops.
Zeros at the end of the decimal do not go on the longer line.
8.1 × 10⁴
Answer: 8.1 × 10⁴
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.
5.7 × 10⁻¹
Answer: 5.7 × 10⁻¹
1,200,000 has an implied decimal at the end of the number.
Swoop the decimal point left until one digit is in front of it. That is 6 swoops.
Write digit . stuff × 10 to the number of swoops.
Zeros at the end of the decimal do not go on the longer line.
1.2 × 10⁶
Answer: 1.2 × 10⁶
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.
3.08 × 10⁻⁴
Answer: 3.08 × 10⁻⁴
In a × 10ⁿ, the coefficient is a.
Scientific notation is a × 10ⁿ.
The coefficient is a. It is at least 1 and less than 10.
In 5 × 10², the coefficient is 5.
Answer: 5
Scientific notation is a × 10ⁿ.
The coefficient is a. It is at least 1 and less than 10.
In 6 × 10³, the coefficient is 6.
Answer: 6
Scientific notation is a × 10ⁿ.
The coefficient is a. It is at least 1 and less than 10.
In 4.7 × 10⁻², the coefficient is 4.7.
Answer: 4.7
Scientific notation is a × 10ⁿ.
The coefficient is a. It is at least 1 and less than 10.
In 9.05 × 10⁵, the coefficient is 9.05.
Answer: 9.05
Scientific notation is a × 10ⁿ.
The coefficient is a. It is at least 1 and less than 10.
In 1 × 10⁻⁴, the coefficient is 1.
Answer: 1
Scientific notation is a × 10ⁿ.
The coefficient is a. It is at least 1 and less than 10.
In 3.2 × 10⁷, the coefficient is 3.2.
Answer: 3.2
Need help with scientific notation?
Book a Session with Amy