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Unit 9: Decimals

Decimals as another way to write a fraction, compared, rounded, and pushed through all four operations.

8 topics · 32 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

What a Decimal Actually Is

  1. How it worksWalk me through turning 3 tenths of a pizza into the decimal 0.3 using a place value chart.
  2. Common mistakeWhy isn't 3.5 the same as having 3 of one thing and 5 of another separate thing?
  3. Going furtherWhat happens to the value of the digit 4 if you move it from 0.4 to 0.04?
Your turn1 of 2
Nina has 7 tenths of a metre of ribbon (0.7 metres). If that same digit 7 moves one place right into the hundredths place instead, what is its new decimal value?

Decimal Place Value

  1. How it worksWalk me through naming the tenths, hundredths, and thousandths places in the decimal 4.256.
  2. Worked exampleFind the value of the digit 8 in the decimal 3.087.
  3. Worked exampleFind how many hundredths are in the decimal 0.64.
  4. Common mistakeWhy doesn't the 3 in the hundredths place of 0.23 mean 3 wholes the way the 3 in 23 does?
  5. Going furtherWhat happens to a decimal's value if you erase a zero from the middle, like turning 0.205 into 0.25?
Your turn1 of 2
A coin jar holds 7 hundredths of a dollar in loose change. Written as a decimal, what is that amount worth?

Comparing and Ordering Decimals

  1. How it worksWalk me through lining up the decimal points in 0.7 and 0.65 to compare them place by place.
  2. Common mistakeWhy isn't 0.5 smaller than 0.45 just because 0.5 has fewer digits after the point?
  3. Worked exampleFind which is longer, a ribbon that is 0.6 meters or a ribbon that is 0.45 meters.
  4. Going furtherWhat happens when you compare 0.500 and 0.5 after adding extra zeros on the end?
Your turn1 of 2
Leo's bike ride was 0.72 kilometres and Priya's was 0.678 kilometres. What is the bigger of the two distances?

Rounding Decimals

  1. How it worksWalk me through rounding 2.463 to the nearest hundredth by checking the digit after it.
  2. Going furtherWhat changes about your answer if you round 2.463 to the nearest tenth instead of the nearest hundredth?
  3. Ties togetherHow does rounding decimals connect to rounding whole numbers to the nearest ten or hundred?
Your turn1 of 2
A runner's time was 6.683 seconds. Round that time to the nearest hundredth of a second.

Adding and Subtracting Decimals

  1. How it worksWalk me through stacking 3.6 and 2.45 with the decimal points lined up before adding.
  2. Common mistakeWhy doesn't lining up the last digits instead of the decimal points work for adding 4.2 and 1.35?
  3. Worked exampleFind the total cost of a toy that costs 4 dollars and 25 cents plus a snack that costs 1 dollar and 50 cents.
  4. Worked exampleFind the answer to 7.8 minus 3.45.
  5. Going furtherWhat happens if you add 2.6 and 3 when 3 has no decimal part written at all?
Your turn1 of 2
Sam buys a toy that costs 14 dollars and 64 cents, and a snack that costs 19 dollars and 28 cents. What is the total cost?

Multiplying Decimals

  1. How it worksWalk me through multiplying 2.3 by 1.4 as whole numbers first and placing the decimal point last.
  2. Worked exampleFind the total price of 3 candy bars that each cost 1 dollar and 25 cents.
  3. Common mistakeWhy doesn't multiplying 0.2 by 0.3 give you 0.6 instead of 0.06?
  4. Ties togetherHow does multiplying decimals connect to multiplying fractions like 2 tenths by 3 tenths?
Your turn1 of 2
Ben buys 7 candy bars that each cost 4 dollars and 92 cents. What is the total price?

Dividing Decimals

  1. Worked exampleFind the answer to 9.6 divided by 1.2.
  2. Common mistakeWhy doesn't dividing 5 by 0.5 give you an answer smaller than 5?
  3. Going furtherWhat happens to the division problem if you multiply both 6.4 and 0.8 by 10 before dividing?
Your turn1 of 2
A ribbon that is 14.52 metres long is cut into pieces that are each 2.74 metres long. How many pieces does it make?

How Decimals and Fractions Are the Same Idea

  1. How it worksWalk me through turning 3 fifths into a decimal by dividing 3 by 5.
  2. Common mistakeWhy can't every fraction be turned into a decimal that stops, like the way 1 third becomes 0.333 forever?
  3. Worked exampleFind the decimal that equals 7 eighths.
  4. Going furtherWhat happens when you try to turn 1 seventh into a decimal instead of a fraction like 1 fourth?
  5. Ties togetherHow does turning a fraction into a decimal connect to dividing the top number by the bottom number?
Your turn1 of 2
Tom read 2 over 8 of his book. Write that amount as a decimal.