Decimals and Place Value
Money. Baseball batting averages. Your height. Your weight. Most of the numbers you see in real life aren't whole numbers — they're **decimals**. A decimal is a number that has a piece smaller than 1. The secret to understanding them is **place value**: every digit has a job based on where it sits.
Place value: left of the decimal point
You already know this from whole numbers:\n\nIn **4,382**:\n- 4 is in the **thousands** place\n- 3 is in the **hundreds** place\n- 8 is in the **tens** place\n- 2 is in the **ones** place\n\nEach place is 10 times bigger than the place to its right.
Place value: right of the decimal point
The pattern keeps going on the right side — but each place gets **smaller** by 10 times.\n\nIn **7.385**:\n- 7 is in the **ones** place\n- 3 is in the **tenths** place (3/10)\n- 8 is in the **hundredths** place (8/100)\n- 5 is in the **thousandths** place (5/1000)\n\nSo 7.385 = 7 + 3/10 + 8/100 + 5/1000. The decimal point is the boundary between "whole" and "parts smaller than whole."
In the number 4.27, what is the value of the 2?
Decimals and fractions (CCSS 4.NF.6)
Every decimal can be written as a fraction, and many fractions can be written as decimals:\n\n- 0.5 = 5/10 = 1/2\n- 0.25 = 25/100 = 1/4\n- 0.1 = 1/10\n- 0.01 = 1/100\n- 0.75 = 75/100 = 3/4\n\nThey're the same number written two ways. Sometimes one way is easier. For money, decimals are easier ($0.75 is clearer than 3/4 of a dollar). For recipes, fractions are often easier (1/2 cup is clearer than 0.5 cup).
Which decimal is the same as the fraction 3/10?
Comparing decimals (4.NF.7)
Compare decimals digit-by-digit from LEFT to RIGHT — same as whole numbers, with one trick.\n\nCompare 0.4 and 0.35:\n\nA common mistake is to think 0.35 is bigger because 35 > 4. **Wrong!** 0.35 is thirty-five hundredths. 0.4 is four tenths, which equals forty hundredths. 40 > 35, so **0.4 > 0.35**.\n\nTrick: if needed, add zeros to the right of a decimal so they have the same number of places:\n- 0.4 = 0.40\n- 0.35 = 0.35\nNow compare 40 vs 35. Easy — 0.40 > 0.35.
Which is larger: 0.6 or 0.58?
Decimals and money
Money is decimals in disguise:\n- $1.00 = one dollar (1 whole)\n- $0.10 = one dime (1 tenth of a dollar)\n- $0.01 = one penny (1 hundredth of a dollar)\n- $0.25 = a quarter = 25 pennies = 25 hundredths of a dollar\n\nBecause money comes in dollars and cents (hundredths of a dollar), you only see two decimal places in prices. But all decimal math works the same way.
Shopping with decimals
With a grown-up, look at a grocery store flyer or website. Pick 3 items. Write their prices as decimals. Then: (1) which is most expensive? (2) which is least? (3) what's the total cost of all 3? Check by lining up the decimal points vertically before adding — that's the key to decimal addition.
Place value draw
Draw a place value chart with these columns: thousands, hundreds, tens, ones, tenths, hundredths, thousandths. Place this number in it: 2,074.516. Read it aloud: "Two thousand seventy-four AND five hundred sixteen thousandths." The word "and" always tells you where the decimal point is.
What is the decimal 0.25 equal to as a fraction?
Decimals are everywhere in daily life — money, measurements, sports stats, scientific data. Once you understand place value, decimals are just as predictable as whole numbers. Stick with the patterns and you'll use decimals confidently for the rest of your life.
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