Decimal Place Value: Understanding Tenths, Hundredths, and Thousandths on the SAT

The decimal place value system extends left and right from the ones place. Left of the decimal: ones, tens, hundreds. Right: tenths (0.1), hundredths (0.01), thousandths (0.001). The most common error is confusing place values, like reading 0.4 as "4 hundredths" when it is "4 tenths," or multiplying by 10 and shifting the decimal wrong, so 0.5×10 becomes 0.50 instead of 5. Preventing these errors requires explicit, careful decimal work on SAT problems.

Build a decimal-checking routine: whenever you work with decimals, explicitly state the place value (0.5 = 5 tenths, 0.05 = 5 hundredths) and trace your decimal shifts carefully. After multiplying or dividing decimals, count decimal places explicitly: 0.5×0.2 has (1+1)=2 decimal places total, so the answer is 0.10. This explicit tracking prevents errors on the SAT.

Multiplication: when you multiply decimals, count total decimal places in both factors and place that many in the product. For example, 0.5×0.3=(5×3)÷(10×10)=15÷100=0.15. Division: when you divide by a decimal, multiply both dividend and divisor by 10 until the divisor is a whole number. For example, 0.5÷0.2=(5÷2)=2.5. Ordering: when you compare decimals, align decimal points and compare digit by digit. For example, 0.5>0.05 because 5 tenths > 5 hundredths. Each operation has a specific routine; master the routine so you execute correctly on the SAT.

Practice these three operations on 10 decimal problems. Time yourself: you should complete all 10 in under five minutes. Once these routines are automatic, decimal problems become reliable points on the SAT.

Converting decimals to fractions requires understanding place value. 0.5=5/10=1/2, 0.25=25/100=1/4, 0.75=75/100=3/4, 0.333...=1/3. The denominator is determined by the decimal place value: one decimal place means denominator 10, two decimal places mean denominator 100, three mean denominator 1000. These conversions often make SAT problems easier to solve, so practice them until automatic.

Practice converting 10 decimals to fractions: 0.6, 0.35, 0.125, 0.8, 0.45, 0.7, 0.05, 0.2, 0.9, 0.04. For each, identify the denominator by place value, then reduce to lowest terms. Time yourself: all 10 should take under 90 seconds once you know the routine on the SAT.

Problem 1: If you buy an item for $5.50 and pay with $10, how much change do you get? (Answer: $10-$5.50=$4.50.) Problem 2: What is 0.4×0.3? (Answer: 1+1=2 decimal places, so 4×3=12 becomes 0.12.) Problem 3: Put in order from least to greatest: 0.5, 0.05, 0.505. (Answer: 0.05<0.5<0.505 because 5 hundredths < 5 tenths < 505 thousandths.) Problem 4: Simplify 0.4÷0.02. (Answer: multiply both by 100 to get 40÷2=20.)

Work through these four problems using the place value and operations routines. Then practice 20 more SAT decimal problems from your test materials. By test day, decimal work will feel automatic and error-free on the SAT.