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## Place Value

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**Expanded Form**4567 • 5 6 7 4000+500+60+7 Four-thousand five-hundred sixty-seven.**Decimal Place Value*****If it ends in “th”, it’s to the right of the decimal; notice there’s no “oneths” place.**Digits – 0,1,2,3,4,5,6,7,8,9**1,274.9835 • What digit is in the tenths place? • What digit is in the thousandth place? • What digit is in the hundreds place? • What digit is in the ones/units place? • What digit is in the hundredths place?**Digits – 0,1,2,3,4,5,6,7,8,9**1,274.9835 • What digit is in the tenths place? 9 • What digit is in the thousandth place? 3 • What digit is in the hundreds place? 2 • What digit is in the ones/units place? 4 • What digit is in the hundredths place? 8**Rounding**Rounding lets you estimate an answer. This can be useful for process of elimination and for checking an answer for reasonableness. Procedure: • Underline the digit in the place to which you are rounding. • If the digit to the right of the underlined digit is greater than or equal to 5, add 1 to the underlined digit. If the digit to the right of the underlined digit is less than 5, leave the underlined digit as it is. 3. Change the digits to the right of the underlined digit to zeros. Note that zeroes to the right of the decimal are not necessary unless they are holding a place value (there are non-zero numbers after them).**Round 6,175,342**To the nearest thousand:**Round 6,175,342**To the nearest thousand: • Step 1 – underline the thousands place 6,175,342 • Step 2 – add one or leave the same 6,175,342 • Step 3 – Replace digits to the right with zeroes 6,175,000 So 6,175,342 rounded to the nearest thousand is 6,175,000.**Round 6,175,342**To the nearest hundred: To the nearest million: To the nearest ten: To the nearest ten-thousand:**Round 6,175,342**To the nearest hundred: 6,175,300 To the nearest million: 6,000,000 To the nearest ten: 6,175,340 To the nearest ten-thousand: 6,180,000**Rounding Decimals**Round 346.9485 To the nearest tenth:**Rounding Decimals**Round 346.9485 To the nearest tenth:**Round 346.9485**To the nearest thousand: • Step 1 – underline the tenths place 346.9485 • Step 2 – add one or leave the same 346.9485 • Step 3 – Replace digits to the right with zeroes 346.9000 So 346.9485 rounded to the nearest tenth is 346.9 *Note that the final zeroes are removed – they are not necessary if they come after the decimal and there are no non-zero numbers after them.**Round 1,890,923.0992:**• To the nearest 10th: • To the nearest million: • To the nearest hundredth: • To the nearest thousandth: • To the nearest thousand:**Round 1,890,923.0992:**• To the nearest 10th: 1,890,923.0992 • 1,890,923.1 • To the nearest million: 1,890,923.0992 • 2,000,000.0000 or 2,000,000 • To the nearest hundredth: 1,890,923.0992 • 1,890,923.1 (note that the added one is carried) • To the nearest thousandth:1,890,923.0992 • 1,890,923.099 • To the nearest thousand: • 1,891,000.0000 or 1,891,000**You should now be able to work out the place value and**rounding problems on page 110. • Next up: working with decimals