By Michelle Brunet • Updated Aug 30, 2022

When you transition from whole numbers to decimals, the arithmetic can feel daunting. In reality, decimals are simply fractions or percentages expressed in a familiar format—think of money, where the dollars are left of the decimal point and cents to the right. For addition and subtraction, the rule is simple: align the decimal points and keep them in the same position in the result. Multiplication and division are a bit trickier, but once you master a few systematic steps, you’ll shift decimal points with confidence.

Step 1: Multiplying by Powers of Ten

Move the decimal point to the right when multiplying a decimal by a power of ten (10, 100, 1,000, etc.). The number of zeros in the power of ten tells you how many places to shift. For example:

• 1.234 × 100 → 123.4 (two zeros → two places)
• 4.568 × 10 → 45.68
• 0.876 × 1,000 → 876

Step 2: Dividing by Powers of Ten

Move the decimal point to the left when dividing by a power of ten. Count the zeros to determine the shift, but in the opposite direction. Example:

• 456.89 ÷ 10 → 45.689 (one zero → one place to the left)

Step 3: Multiplying Two Decimals

Ignore the decimal points during the multiplication process. Treat the numbers as whole integers, then place the decimal point in the final product. The total number of places after the decimal equals the sum of the places to the right of each original decimal. Example:

• 2.34 × 4.5 → 10530 → 10.530 (three places total)

Step 4: Long Division with Decimals

When performing long division, first shift the decimal point of the divisor (the number outside the division bar) completely to the right so it becomes an integer. Apply the same shift to the dividend (the number inside the bar). For instance, dividing 456.7 by 2.34:

• Shift divisor: 2.34 → 234 (two places)
• Shift dividend: 456.7 → 45670 (two places)
• Proceed with standard long division, placing the decimal point in the quotient directly above the original decimal in the dividend.

If the divisor lacks a decimal point, no shifting is required, even if the dividend contains one.

Follow these guidelines to handle decimal arithmetic accurately and confidently.