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Multiplicative Patterns on thePlace Value ChartUnit 2 Lesson 1

Multiplicative Patterns on the Place Value ChartStudents will be able to: Understand the place value system. Recognize that a digit in one place is ten times bigger asmuch as that to its right. Recognize that a digit in one place is ten times smaller asmuch as that to its right. Complete place value charts from millions tothousandths. Compose and decompose units by applying theknowledge of 10 and 1/10 times depending on the digit’splace value.

Multiplicative Patterns on the Place Value ChartKey Vocabulary:Place ValuePlace Value ChartPowers of TenDigit

Multiplicative Patterns on the Place Value ChartPlace Value SystemAll numbers are made up of digits from 1 to 9. Each ofthese digits has its place and value. The place value of aparticular digit relies on the its position. The last digitstarts with ones, the next would be tens, and so on.

Multiplicative Patterns on the Place Value ChartPlace Value SystemThe place of a digit is 10 times bigger than the placevalue of the digit to its right. For example, the placevalue of 4 in the picture is ten times bigger than that of5.

Multiplicative Patterns on the Place Value ChartPlace Value SystemThe place of a digit is 10 times bigger than the placevalue of the digit to its right.Example 1:Hundreds 10 x OnesOne thousands 10 x Hundreds

Multiplicative Patterns on the Place Value ChartPlace Value SystemSimilarly, the place of a digit is 10 times smaller or𝟏𝟏𝟎than the place value of the digit to its left.Example 2:Thousands 𝟏𝟏𝟎x Ten ThousandsHundred Thousands 𝟏𝟏𝟎x Millions

Multiplicative Patterns on the Place Value ChartSample Problem 1:Determine whether the place value of 4 is ten timessmaller or bigger than the place value of 6.a. 123, 465b. 64, 389c. 154, 678

Multiplicative Patterns on the Place Value ChartSample Problem 1:Determine whether the place value of 4 is ten timessmaller or bigger than the place value of 6.a. 123, 465b. 64, 389c. 154, 678Solution:a. Ten times biggerc. Ten times biggerb. Ten times smaller

Multiplicative Patterns on the Place Value ChartSample Problem 2:Complete the sentences to make them true.a. Hundreds Tensb. Ten Thousands Hundred Thousandsc. Thousands Hundreds

Multiplicative Patterns on the Place Value ChartSample Problem 2:Complete the sentences to make them true.a. Hundreds Tensb. Ten Thousands Hundred Thousandsc. Thousands HundredsSolution:a. Hundreds 10 x Tensb. Ten Thousands 1/ 10 x Hundred Thousandsc. Thousands 10 x Hundreds

Multiplicative Patterns on the Place Value ChartDecimal Place ValuesDecimals is expressed in the form of whole number thena dot and followed by one or more digits representingthe decimal places. The decimal places also representthe digits’ places as shown below.

Multiplicative Patterns on the Place Value ChartValue of Digits Based on their Place ValuesWe can read and write out a particular digits’ exact valueby locating its place value.Example:To find the value of 3 in 53467, first locate the placevalue of 3. In this case, it’s ten thousands. Hence, thevalue of 3 is 3 ten thousands or 30 thousands.Using the same idea, the value of 4 in 23.647 is 4hundredths.

Multiplicative Patterns on the Place Value ChartSample Problem 3:Determine the value of 5 from given the numbers below.a. 156.78b. 20.865c. 45678.92d. 2.386759

Multiplicative Patterns on the Place Value ChartSample Problem 3:Determine the value of 5 from given the numbers below.a. 156.78b. 20.865c. 45678.92d. 2.386759Solution:a. 5 tensb. 5 thousandthsc. 5 thousandsd. 5 hundred thousandths

Multiplicative Patterns on the Place Value ChartPlace Value ChartsUsing place value charts make it easier to know the placevalues of all the given digits.The chart above shows the place value chart for wholenumbers from ones to millions. The values of the digitscan also be found by multiplying the digit to its placevalue.

Multiplicative Patterns on the Place Value ChartPlace Value ChartsFor example, the digits of 405 789 can be filled in thetable as shown below.

Multiplicative Patterns on the Place Value ChartPlace Value ChartsA similar place value chart shown below can be made fornumbers with decimal places.

Multiplicative Patterns on the Place Value ChartPlace Value ChartsThis means that for 309.16, we can fill in the place valuechart shown below.

Multiplicative Patterns on the Place Value ChartSample Problem 4:Fill in the place value chart below for the following numbers.1.2.

Multiplicative Patterns on the Place Value ChartSample Problem 4:Fill in the place value chart below for the following numbers.1.2.

Multiplicative Patterns on the Place Value ChartMultiplying and Dividing Numbers by 10, 100, and 1000Multiplying and dividing numbers by 10, 100, and 100 canbe easily be done by moving the place values of the digitsto the left or right, depending on the operation.Observe the three numbers 1.567, 15.67, and 156.7. Ifwe place each of the digits on a place value chart, we’llhave the following.

Multiplicative Patterns on the Place Value ChartMultiplying and Dividing Numbers by 10, 100, and 1000Notice that as the digits move one place to left, the valueincreases ten times.

Multiplicative Patterns on the Place Value ChartMultiplying and Dividing Numbers by 10, 100, and 1000This means that we have:

Multiplicative Patterns on the Place Value ChartMultiplying and Dividing Numbers by 10, 100, and 1000Using the same idea, we can easily divide numbers by 10 bymoving the digits’ decimal place one step to the right.

Multiplicative Patterns on the Place Value ChartMultiplying and Dividing Numbers by 10, 100, and 1000Using 246.8, 24.68, and 2.468, as an example as shownbelow.

Multiplicative Patterns on the Place Value ChartSample Problem 5:Move the place values of the digits to solve the followingproblems.1. 21.034 x 100 3. 137.48 10 2. 456.089 x 10 4. 9105.123 100

Multiplicative Patterns on the Place Value ChartSample Problem 5:Move the place values of the digits to solve the followingproblems.1. 21.034 x 100 3. 137.48 10 2. 456.089 x 10 4. 9105.123 100

Multiplicative Patterns on the Place Value ChartPowers of 10Recall that we have10 x 1 10 10110 x 10 100 10210 x 10 x 10 1000 103This pattern continues for powers of 10.

Multiplicative Patterns on the Place Value ChartPowers of 10As a matter of fact, if we need to multiply 10 n times toitself, we’ll have

Multiplicative Patterns on the Place Value ChartMultiplying and Dividing Numbers by a Power of TenUsing our knowledge about powers of ten, we can multiplyand divide numbers (both whole numbers and those withdecimals) by moving the place values of the numbers.Move the places to the right depending on power of 10 orthe number of zeroes present.

Multiplicative Patterns on the Place Value ChartMultiplying and Dividing Numbers by a Power of TenExample:348 x 1000For whole numbers, we start moving starting from theones place. Since 1000 103 and has three zeroes, we movethree places from 8 to the right.This means that 348 x 1000 348, 000.

Multiplicative Patterns on the Place Value ChartMultiplying and Dividing Numbers by a Power of TenA similar process can be performed when multiplyingdecimals by a power of ten.Example:234.56 x 100Start from the decimal point this time when moving theplace values. Place the decimal point to its new positionafter moving.

Multiplicative Patterns on the Place Value ChartMultiplying and Dividing Numbers by a Power of TenSince 100 102 or has two zeroes present, we move thedecimal point two places to the right.This gives us 23.456 x 100 2345.6 now.

Multiplicative Patterns on the Place Value ChartMultiplying and Dividing Numbers by a Power of TenUse the same process when dividing numbers by powers often. The only difference is to move the place values tothe left instead.Example:This means that 33548 10000 3.3458.

Multiplicative Patterns on the Place Value ChartSample Problem 6:Find the product or quotient of the following by moving thedecimal places.1. 5.17895 x 10000 3. 56374.8 10000 2. 30.348 x 1000 4. 4572394.23 10000

Multiplicative Patterns on the Place Value ChartSample Problem 6:Solution:1. 5.17895 x 10000 51789.52. 30.348 x 1000 303483. 56374.8 10000 5.637484. 4572394.23 10000 457.239423

Multiplicative Patterns on the Place Value ChartFractions with Denominators as Powers of TenChanging fractions with denominators as powers of ten todecimals can be done easily by moving the place values ofthe digits as we have done in the previous section.Remember that given a fraction A/B, we can express it asA B to find its decimal counterpart.

Multiplicative Patterns on the Place Value ChartFractions with Denominators as Powers of TenSo, if B is a power of ten, we can simply move the decimalplaces to the left depending on the number of zeroes orits power.Example:

Multiplicative Patterns on the Place Value ChartSample Problem 7:Change the following fractions to decimals.1. 34 567/ 100 3. 4 334 098/ 10000 2. 5 433/ 1000 4. 9 823 743/ 100000

Multiplicative Patterns on the Place Value ChartSample Problem 7:Solution:1. 34 567/ 100 34 567 100 345.672. 5433/100 5 433 1000 5.4333. 4 334 098 / 10000 4 334 098 10000 433.40984. 9 823 743/ 100000 9 823 743 100000 98.23743

Jun 02, 2020 · starts with ones, the next would be tens, and so on. Place Value System. Multiplicative Patterns on the Place Value Chart The place of a digit is 10 times bigger than the place value of the digit to its right. For example, the place . Hundreds 10 x Ones One thousands 10 x Hundreds Place Value