Number Sense and Operations with Whole Numbers, Fractions, and Decimals
The Number Sense and Operations domain is the broadest strand on Grade 5 FAST Math. It tests place value through thousandths, reading and writing decimals in standard, expanded, and word form, comparing and rounding decimals, multi-digit whole-number multiplication and division, and addition, subtraction, and multiplication of decimals. Whole-number fluency and decimal place value also feed into geometry and data items, so mistakes here surface elsewhere.
Place value and decimal operations
- A digit in the thousandths place has value 1/1000; moving one place left multiplies its value by 10.
- Compare decimals by aligning place values and comparing digits left to right. Because 0.4 = 0.400, 0.45 > 0.405.
- To add or subtract decimals, line up decimal points and annex zeros so both numbers have the same number of decimal places.
- Multiply decimals as if they were whole numbers, then place the decimal point so the product has as many decimal places as the two factors combined.
- Dividing by 10, 100, or 1,000 shifts digits right; multiplying shifts digits left.
Whole-number operations
Use the standard algorithm for multiplication and division. When a division leaves a remainder and the context calls for an exact quotient, record the remainder as a fraction or decimal. Estimate first: 4,187 ÷ 21 is about 4,200 ÷ 20 = 210, so a quotient near 199 is reasonable.
Worked example
Find 2.4 × 0.35.
- Ignore the decimals: 24 × 35 = 840.
- Count decimal places: 2.4 has one, 0.35 has two, for three places total.
- Place the point three places from the right: 0.840, or 0.84. Check with estimation: 2.4 × 0.35 is about 2 × 0.3 = 0.6, and 0.84 is close.
Traps that cost marks
- Lining up decimal points when multiplying. Multiplication does not require it, and doing so often misplaces the product.
- Forgetting to annex zeros in subtraction such as 5.2 − 1.875.
- Counting decimal places in only one factor.
- Reporting a remainder as the answer when the question asks for a decimal quotient.
- Rounding too early in a multi-step problem; keep exact values until the final step.