Arithmetic | 10 of 17
Prerequisites: Numbers and Place Value, Division. Enables: Ratios, Rates, and Proportions.
Decimals are base-ten fractions.
Examples:
$$
0.4 = \frac{4}{10}
$$
$$
0.37 = \frac{37}{100}
$$
$$
0.125 = \frac{125}{1000}
$$
Decimal place values
| Place | Fraction | Decimal example |
|---|---|---|
| Tenths | $\frac{1}{10}$ | $0.1$ |
| Hundredths | $\frac{1}{100}$ | $0.01$ |
| Thousandths | $\frac{1}{1000}$ | $0.001$ |
| Ten-thousandths | $\frac{1}{10000}$ | $0.0001$ |
Adding and subtracting decimals
Line up decimal points.
Example:
$$
8.6 + 12.47 = 8.60 + 12.47 = 21.07
$$
Example:
$$
9.3 - 4.86 = 9.30 - 4.86 = 4.44
$$
Multiplying decimals
Multiply as whole numbers, then place the decimal according to the total number of decimal places in the factors.
Example:
$$
1.2 \cdot 0.34
$$
Ignore decimals first:
$$
12 \cdot 34 = 408
$$
There are three total decimal places, so:
$$
1.2 \cdot 0.34 = 0.408
$$
Dividing decimals
Move the decimal in the divisor to make it a whole number. Move the decimal in the dividend by the same number of places.
Example:
$$
4.56 \div 0.12
$$
Multiply both by $100$:
$$
456 \div 12 = 38
$$
Therefore:
$$
4.56 \div 0.12 = 38
$$
Converting decimals to fractions
Write the decimal over the correct power of ten, then simplify.
Example:
$$
0.75 = \frac{75}{100} = \frac{3}{4}
$$
Converting fractions to decimals
Divide numerator by denominator.
Example:
$$
\frac{7}{8}=7\div8=0.875
$$
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