Number and Operations in Base Ten: Place Value, Whole Numbers, and Decimals
Number and Operations in Base Ten in Grade 5 covers place value through thousandths, powers of ten, multi-digit whole-number computation, and the four operations with decimals to hundredths.
Place value and powers of ten
Each place is 10 times the place to its right and one-tenth of the place to its left: 0.1 = 1/10, 0.01 = 1/100, 0.001 = 1/1000. Multiplying by 10, 100, or 1,000 shifts digits left; dividing shifts them right. So 3.75 × 100 = 375 and 3.75 ÷ 10 = 0.375. Exponents record the pattern: 3.75 × 10² = 375.
Comparing and rounding
Align place values and compare from the left, annexing zeros as needed: 0.45 > 0.405 because the hundredths digits are 5 and 0. To round, look at the digit to the right of the rounding place; 5 or more rounds up, so 6.847 rounded to hundredths is 6.85.
Computing
Multiply multi-digit numbers with the standard algorithm and divide up to four-digit dividends by two-digit divisors; estimate to check, as in 4,812 ÷ 62 ≈ 4,800 ÷ 60 = 80. For decimals, align points to add or subtract; multiply as whole numbers, then count the total decimal places; in division, move the divisor’s point to make it whole and move the dividend’s point the same number of places.
Worked example
4.6 × 0.35. Ignore the decimal points: 46 × 35 = 1,610. The factors have one and two decimal places, three total, so place the point three places from the right: 1.610 = 1.61. Estimate to confirm: 5 × 0.3 = 1.5, which is close to 1.61.
Traps that cost marks
- Not aligning decimal points when adding or subtracting.
- Counting decimal places from only one factor.
- Thinking 0.45 < 0.5 because 45 < 5.
- Moving the divisor’s decimal point but not the dividend’s.