Decimal notation, operations, relationship to fractions
Middle School Bridge • 6-8
Money uses decimals every day: $3.75 means 3 dollars and 75 hundredths of a dollar. Decimals are simply another way to write fractions whose denominators are powers of 10. Understanding how decimals work -- and how they connect to fractions -- opens the door to working fluently with all kinds of numbers.
Each digit in a decimal number holds a specific position, and that position determines its value. The decimal point separates the whole-number part from the fractional part.
| Position | Name | Value |
|---|---|---|
| Left of decimal | Ones | 1 |
| 1st right of decimal | Tenths | 1⁄10 |
| 2nd right of decimal | Hundredths | 1⁄100 |
| 3rd right of decimal | Thousandths | 1⁄1000 |
For example, in 4.365: the 4 is in the ones place, 3 is in the tenths place (3 × 0.1 = 0.3), 6 is in the hundredths place (6 × 0.01 = 0.06), and 5 is in the thousandths place (5 × 0.001 = 0.005).
Convert 0.35 to a fraction.
Convert 3⁄8 to a decimal.
Adding and subtracting: Line up the decimal points vertically, fill empty places with zeros, then add or subtract as with whole numbers.
Multiplying: Multiply as if there were no decimal points. Then count the total number of decimal places in both factors and place the decimal point that many places from the right in the product.
Dividing: If the divisor is a decimal, move the decimal point in both the divisor and dividend to the right until the divisor is a whole number. Then divide normally.
Compute 2.4 × 0.13.
So 2.4 × 0.13 = 0.312.
When adding or subtracting decimals, some students line up the last digits instead of the decimal points. Always align on the decimal point. For example, to compute 3.5 + 12.75, write it as 3.50 + 12.75, not 3.5 underneath 12.75 with the 5s aligned.
1. Convert 0.625 to a fraction in lowest terms.
625⁄1000. GCF = 125. 625 ÷ 125⁄1000 ÷ 125 = 5⁄8.
2. Convert 7⁄20 to a decimal.
7 ÷ 20 = 0.35.
3. Compute 5.62 + 3.8.
Align: 5.62 + 3.80 = 9.42.
4. Compute 1.5 × 0.4.
15 × 4 = 60. Total decimal places: 2. So 0.60 = 0.6.
5. Compute 7.2 ÷ 0.9.
Move decimal one place right in both: 72 ÷ 9 = 8.
Decimals are fractions written using place value, where each position to the right of the decimal point represents a power of 10 in the denominator. Converting between decimals and fractions is a matter of reading the place value. For operations, align decimal points when adding or subtracting, count total decimal places when multiplying, and shift the decimal when dividing.