To add or subtract numbers in scientific notation,
the numbers all need to be multiplied by the same power of 10.
First, write both numbers so that they are multiplied by the same power of 10.
One way to do this is to move the decimal point in 9.9 × 10
3 one place to the right, and then decrease the power of 10 by 1 to keep the value of the number the same.
(1.58 × 102) + (9.9 × 103) = (1.58 × 102) + (99 × 102)
Next, factor out 10
2, then add.
| (1.58 × 102) + (99 × 102) | = | (1.58 + 99) × 102 |
| = | 100.58 × 102 |
Write the number in scientific notation by moving the decimal point 2 places to the left and increasing the power of 10 by 2.
100.58 × 102 = 1.0058 × 104
The number can also be written in standard notation by moving the decimal point 2 places to the right.
100.58 × 102 = 10,058
Use properties of operations and exponents to
multiply or divide numbers in scientific notation.
First, divide using properties of operations and exponents.
| (1.887 × 10-5) ÷ (3.7 × 10-2) | = | (1.887 ÷ 3.7) × (10-5 ÷ 10-2) |
| = | 0.51 × 10[-5 - (-2)] |
| = | 0.51 × 10-3 |
Write the number in scientific notation by moving the decimal point one place to the right and decreasing the exponent of 10 by 1.
0.51 × 10-3 = 5.1 × 10-4
The number can also be written in standard notation by moving the decimal point 3 places to the left.
0.51 × 10-3 = 0.00051
First, multiply using properties of operations and exponents.
| 0.0051 × (3.8 × 10-3) | = | (0.0051 × 3.8) × 10-3 |
| = | 0.01938 × 10-3 |
Write the number in scientific notation by moving the decimal point two places to the right and decreasing the exponent of 10 by 2.
0.01938 × 10-3 = 1.938 × 10-5
The number can also be written in standard notation by moving the decimal point 3 places to the left.
0.01938 × 10-3 = 0.00001938
8th Grade Math - Scientific Notation Lesson