7th Grade Math · Unit 2
Positive powers of 10. Swoop the decimal point to the right, and fill empty places with zeros.
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.
Positive exponents swoop right
The exponent is the number of swoops.
Swoop the decimal point to the right that many times.
Fill each empty place with a zero.
Implied decimal
A whole number such as 1,200 has an implied decimal at the end of the number.
Positive powers of 10. Problems 1–10 have an integer coefficient. Problems 11–20 have a decimal coefficient.
4 × 10³
The exponent is 3, so the decimal point makes 3 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
Answer: 4,000
3.4 × 10⁵
The exponent is 5, so the decimal point makes 5 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
340,000
Answer: 340,000
6 × 10³
The exponent is 3, so the decimal point makes 3 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.
6,000
Answer: 6,000
2 × 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.
20,000
Answer: 20,000
8 × 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.
800
Answer: 800
5 × 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.
500,000
Answer: 500,000
9 × 10³
The exponent is 3, so the decimal point makes 3 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.
9,000
Answer: 9,000
3 × 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.
3,000,000
Answer: 3,000,000
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
4 × 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.
400
Answer: 400
1 × 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.
100,000
Answer: 100,000
8 × 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.
8,000,000
Answer: 8,000,000
2.5 × 10³
The exponent is 3, so the decimal point makes 3 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
2,500
Answer: 2,500
6.1 × 10⁴
The exponent is 4, so the decimal point makes 4 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
61,000
Answer: 61,000
7.8 × 10²
The exponent is 2, so the decimal point makes 2 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
780
Answer: 780
1.2 × 10⁵
The exponent is 5, so the decimal point makes 5 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
120,000
Answer: 120,000
9.4 × 10³
The exponent is 3, so the decimal point makes 3 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
9,400
Answer: 9,400
3.05 × 10⁴
The exponent is 4, so the decimal point makes 4 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
30,500
Answer: 30,500
4.6 × 10⁶
The exponent is 6, so the decimal point makes 6 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
4,600,000
Answer: 4,600,000
8.3 × 10²
The exponent is 2, so the decimal point makes 2 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
830
Answer: 830
5.27 × 10³
The exponent is 3, so the decimal point makes 3 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
5,270
Answer: 5,270
1.9 × 10⁵
The exponent is 5, so the decimal point makes 5 swoops to the right.
Write digit . stuff × 10 to the number of swoops.
190,000
Answer: 190,000
A whole number has an implied decimal at the end. Swoop left. Problems 1–10 have an integer coefficient. Problems 11–20 have a decimal coefficient.
5,000 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.
5 × 10³
Answer: 5 × 10³
1,200 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.
1.2 × 10³
Answer: 1.2 × 10³
40,000 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.
4 × 10⁴
Answer: 4 × 10⁴
700,000 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.
7 × 10⁵
Answer: 7 × 10⁵
3,000 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.
3 × 10³
Answer: 3 × 10³
800,000 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.
8 × 10⁵
Answer: 8 × 10⁵
60 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 1 swoop.
Write digit . stuff × 10 to the number of swoops.
The other digits are zeros, so the longer line stays empty.
6 × 10¹
Answer: 6 × 10¹
9,000,000 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.
9 × 10⁶
Answer: 9 × 10⁶
200 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.
2 × 10²
Answer: 2 × 10²
50,000 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.
5 × 10⁴
Answer: 5 × 10⁴
6,000,000 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.
6 × 10⁶
Answer: 6 × 10⁶
10,000 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.
1 × 10⁴
Answer: 1 × 10⁴
3,400 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.
3.4 × 10³
Answer: 3.4 × 10³
62,000 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.
6.2 × 10⁴
Answer: 6.2 × 10⁴
730 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.
Zeros at the end of the decimal do not go on the longer line.
7.3 × 10²
Answer: 7.3 × 10²
150,000 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.
1.5 × 10⁵
Answer: 1.5 × 10⁵
4,250 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.
4.25 × 10³
Answer: 4.25 × 10³
90,600 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 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.
9.06 × 10⁴
Answer: 9.06 × 10⁴
2,700,000 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.
2.7 × 10⁶
Answer: 2.7 × 10⁶
810 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.
Zeros at the end of the decimal do not go on the longer line.
8.1 × 10²
Answer: 8.1 × 10²
56,300 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.
5.63 × 10⁴
Answer: 5.63 × 10⁴
1,040,000 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.
1.04 × 10⁶
Answer: 1.04 × 10⁶
Write the standard form, then count the zeros after the last nonzero digit.
Write the standard form first. The exponent is the number of swoops.
8 × 10³
The exponent is 3, so the decimal point makes 3 swoops to the right.
8 → 8,000
The last nonzero digit is 8.
The zeros after 8: 3.
Answer: 3
Write the standard form first. The exponent is the number of swoops.
3.84 × 10⁴
The exponent is 4, so the decimal point makes 4 swoops to the right.
3.84 → 38,400
The last nonzero digit is 4.
The zeros after 4: 2.
Answer: 2
Write the standard form first. The exponent is the number of swoops.
5.1 × 10⁶
The exponent is 6, so the decimal point makes 6 swoops to the right.
5.1 → 5,100,000
The last nonzero digit is 1.
The zeros after 1: 5.
Answer: 5
Write the standard form first. The exponent is the number of swoops.
2.7 × 10⁵
The exponent is 5, so the decimal point makes 5 swoops to the right.
2.7 → 270,000
The last nonzero digit is 7.
The zeros after 7: 4.
Answer: 4
Write the standard form first. The exponent is the number of swoops.
6.05 × 10⁴
The exponent is 4, so the decimal point makes 4 swoops to the right.
6.05 → 60,500
The last nonzero digit is 5.
The zeros after 5: 2.
Answer: 2
Write the standard form first. The exponent is the number of swoops.
1.9 × 10⁷
The exponent is 7, so the decimal point makes 7 swoops to the right.
1.9 → 19,000,000
The last nonzero digit is 9.
The zeros after 9: 6.
Answer: 6
Need help with scientific notation?
Book a Session with Amy