Number Sense and Numeration: Place Value, Whole Numbers, Fractions, and Decimals
What you must understand
Grade 5 number sense rests on place value from millions down to thousandths. You must read, write, compare, and order whole numbers and decimals, round to any given place, and convert fluently among fractions, decimals, and mixed numbers. Know that a fraction is a division, that equivalent fractions name the same quantity, and that multiplying or dividing numerator and denominator by the same nonzero number changes the form, not the value. Factors, multiples, primes, and composites support work with common denominators and simplest form. Estimation with benchmarks (0, 1/2, 1) is expected before exact calculation.
Traps to watch
- Comparing decimals by digit count: 0.45 is greater than 0.4, but 0.45 is less than 0.5. Line up place values or think money.
- Reading 3/4 as "three and four" instead of three-fourths.
- Rounding 4.96 to the nearest tenth as 4.9; the hundredths digit 6 pushes the tenths up to 5.0.
- Forgetting that a whole number is a fraction with denominator 1, so 2 = 2/1.
- Assuming a larger denominator means a larger fraction; 1/8 is smaller than 1/3.
Worked example
Order 0.6, 3/5, 0.58, and 7/12 from least to greatest. Convert to decimals: 3/5 = 0.6, 7/12 ≈ 0.583. Compare: 0.58 < 0.583 < 0.6 = 0.6. So the order is 0.58, 7/12, 0.6, 3/5 (the last two are equal).
Rule of thumb
When in doubt, convert everything to the same form (usually decimals to the thousandths place) before comparing.