Decimal Operations Reference Cheat Sheet

Key Facts

• To add or subtract decimals, line up the decimal points and add zeros as placeholders when needed, such as $4.50 - 2.75 = 1.75$.
• When multiplying decimals, multiply as whole numbers first, then place the decimal so the product has the total number of decimal places from both factors.
• For $2.4 \times 0.3$, there are $1 + 1 = 2$ decimal places, so $24 \times 3 = 72$ becomes $0.72$.
• To divide by a decimal, multiply both the divisor and dividend by the same power of $10$ until the divisor is a whole number.
• For $5.6 \div 0.7$, move both decimals one place right to get $56 \div 7 = 8$.
• To round a decimal, look at the digit to the right of the place you are rounding to; if it is $5$ or more, round up.
• The value of a digit depends on its place, so in $3.472$, the $4$ is in the tenths place, the $7$ is in the hundredths place, and the $2$ is in the thousandths place.
• Adding zeros to the end of a decimal does not change its value, so $6.3 = 6.30 = 6.300$.

Vocabulary

Decimal

A decimal is a number written with a decimal point to show parts of a whole.

Decimal point

The decimal point separates the whole-number part from the fractional part of a number.

Place value

Place value tells the value of a digit based on its position in a number.

Tenths

Tenths are the first place to the right of the decimal point, where each unit is worth $\frac{1}{10}$.

Hundredths

Hundredths are the second place to the right of the decimal point, where each unit is worth $\frac{1}{100}$.

Rounding

Rounding replaces a number with a nearby value that is easier to use while keeping it close to the original number.