Where this sits. This is one of the five number families — the arithmetic that a little under half the test is made of, and that every algebra family is built out of. Every family page on this site has the same eight parts, in the same order, so once you know the shape of one you know the shape of all of them. Where a part is empty, it says so.
DrillsFourteen drills for this family, one skill each, ten problems at a timeGo to the drills ↓Fractions written in tenths and hundredths. You already practice these daily — every price is a decimal — and the skills are lining up the point, knowing what each place means, and moving between a decimal and the fraction that says the same thing.
The test hands you a calculator for all but the first few questions, so the arithmetic itself is rarely the hard part. Knowing what the answer should look like, so you can tell when the calculator has been fed the wrong thing, is.
What the test asks in this family
- Decimal place valueQuiz 13 · Decimals Practice
- Reading a decimal aloudQuiz 13 · Decimals Practice
- Comparing and rounding decimalsQuiz 13 · Decimals Practice
- Adding and subtracting decimalsQuiz 14 · Decimals Practice
- Multiplying decimalsQuiz 15 · Decimals Practice
- Dividing by a decimalQuiz 15 · Decimals Practice
- Multiplying and dividing by powers of tenQuiz 15 · Decimals Practice
- Turning a fraction into a decimal, and backQuiz 16 · Decimals Practice
- Repeating decimals, and how to know one is comingQuiz 16 · Decimals Practice
All 9 have something on this site.
Six questions across this family. Type an answer and press Check. You get the reasoning for every one, right or wrong.
- In 5.062, what is the 6 worth? Six hundredths, or 0.06. After the point the places run tenths, hundredths, thousandths. The 6 is in the second place, so it is six hundredths — not six, and not six tenths.
- 3.7 + 12.45 = 16.15. Line up the points, not the right-hand edges. Pad the short one so they match: 3.70 + 12.45. Then add as usual. Lining up the right-hand edges instead would give you 4.94 and a wrong answer, and it is the single most common mistake in this family.
- 0.4 × 0.3 = 0.12, not 1.2. Multiply as though the points were not there: 4 × 3 = 12. Now count the decimal places in the question — one in 0.4 and one in 0.3, so two altogether — and give the answer two: 0.12. Notice it is smaller than either number, because you are taking a part of a part.
- 7.2 ÷ 0.9 = 8. You cannot divide by a decimal comfortably, so slide the point in both numbers by the same amount until the one you are dividing by is whole: 72 ÷ 9. Sliding both keeps the answer the same, in the same way that doubling both numbers in a fraction does.
- Write 3⁄8 as a decimal. 0.375. The fraction bar was always a division sign: three eighths means 3 ÷ 8. Do that division and you get 0.375. This one comes out exact; some, like 1⁄3, run on forever.
- Which is bigger, 0.7 or 0.68? 0.7. The longer number is not the bigger one. Pad the short one so they have the same number of places: 0.70 against 0.68. Now they are the same kind of thing — seventy hundredths against sixty-eight — and 0.7 is clearly ahead.
Missed one? The four decimal quizzes are in Learn it just below, and Quiz 16 shows fractions and decimals writing the same number two ways. Decimals Practice under On paper has 150 problems for the drill.
Want more than these six questions? Flyover I asks about all fourteen families in one sitting and ends in a grid that says where to start; Flyover II asks them again later, with different questions, so you can see what has moved.
- Quiz 13Decimal Place ValueWhat each place after the point is worth.
- Quiz 14Adding and Subtracting DecimalsLining up the point, and why that is the whole trick.
- Quiz 15Multiplying and Dividing DecimalsWhere the point goes in the answer.
- Quiz 16Converting Fractions and DecimalsThe same number, written two ways.
Fourteen short drills, one skill each, in order. Each starts with two worked examples, then gives you ten problems (or five) and the reasoning for every answer. Each one prints, with the answer key on the last page. When you get all ten right, or all five right twice in a row, the drill gets a check mark on the Drills page.
- 4.01Place value: tenths, hundredths, thousandths
- 4.02Read and write decimals in words
- 4.03Compare and order decimals
- 4.04Round decimals
- 4.05Add decimals
- 4.06Subtract decimals
- 4.07Multiply decimals
- 4.08Multiply and divide by 10, 100 and 1,000: move the point
- 4.09Divide a decimal by a whole number
- 4.10Divide by a decimal
- 4.11Decimal to fraction
- 4.12Fraction to decimal, including repeating decimals
- 4.13Estimate with decimals
- 4.14Money problems · calculator allowed
No app for this family yet.
- Decimals Practice · 150 problems: place value, reading a decimal aloud, comparing and rounding, the four operations, multiplying and dividing by 10, 100 and 1,000, and moving between fractions and decimals, repeating decimals included. Answer key at the end. Made to print.
- Khan Academy, math · free videos and practice. Search it for decimals, decimal place value, converting fractions to decimals. These are the clips we start from in class.
- Math Antics · short, plain videos on the basics.
- Light & Salt Learning · free GED classes online, with playlists by topic.
- Get Sum Math · GED math on video, one topic at a time.
- Kaplan GED Test Prep and the McGraw-Hill Mathematical Reasoning Workbook · look up decimals in the contents of either.
On to percents, ratios, and proportion — the test’s workhorse. A percent is a decimal is a fraction, and the three families you have just read run into each other there.