Fractions & Decimals • Topic 4 of 5

Decimals & Place Value

A decimal is a fraction whose denominator is a power of 10, and the position of each digit names that power: tenths, hundredths, thousandths, and so on. So 0.47 is 47/100, and 0.005 is 5/1000. Reading place value cleanly makes rounding and estimation reliable: to round 3.147 to the hundredths place, look at the next digit (7 ≥ 5) and round up to 3.15. Multiplying or dividing by powers of 10 just slides the decimal point — ×100 moves it two places right, ÷1000 moves it three left. When you multiply two decimals, count the total decimal places in the factors and put that many in the answer (0.3 × 0.04 = 0.012, three places). The GRE uses decimals heavily in Data Interpretation and money contexts, and a misplaced decimal point is one of the most common careless errors — say the place value out loud when it matters.

✅ Solved examples

1. What is the digit in the hundredths place of 27.384?
Places after the point: 3 is tenths, 8 is hundredths, 4 is thousandths. The hundredths digit is 8.
2. Round 4.2683 to the nearest hundredth.
Hundredths digit is 6; the next digit is 8 (≥ 5), so round up: 4.27.
3. Compute 0.6 × 0.05.
Multiply 6 × 5 = 30; total decimal places 1 + 2 = 3, so place the point three from the right: 0.030 = 0.03.
4. Quantitative Comparison. Quantity A: 0.4. Quantity B: 0.400. Which is greater?
Trailing zeros do not change value: 0.400 = 0.4. Quantity A = Quantity B; they are equal.

✏️ Practice — try these, take hints as needed

1. What digit is in the thousandths place of 5.9174?
Count places: tenths, hundredths, thousandths.
9, 1, 7.
Third place.
7
2. Round 12.4519 to the nearest tenth.
Tenths digit is 4.
Next digit 5.
Round up.
12.5
3. Compute 0.02 × 0.3.
2 × 3 = 6.
Total 3 decimal places.
Place the point.
0.006
4. Compute 4.5 ÷ 100.
Divide by 100.
Shift point 2 left.
0.045.
0.045
5. Which is greater, 0.089 or 0.1?
Compare tenths first.
0 vs 1 in tenths.
0.1 = 0.100.
0.1

📝 Topic test — 8 questions

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