In other words, the digit 6 in does not mean six but six thousand, because the six is placed in the thousands' place. The place of a digit determines its value.
The comma between thousands and hundreds is added as a separator for easier reading. In some countries an empty space is used instead: 6, is written as 6 These numbers are written in expanded form. Write them the normal way. What would the next bigger place value be after thousands?
What would the next smaller place value be after ones? Nine is in the tenths place. It means We are back to fractions!!! It also has a comma separating the thousands from the other digits for easier reading. To compare 2. Put these decimals in order, starting with the smallest:. The answer is: 3. Place value and ordering decimals Decimal points are used in numbers to separate the whole number from parts of the whole. Place value Place value gives the value of each digit in a number. Hundreds Tens Units.
For example, Brad in Year 6, would interpret. Brad's interpretation of 0. Instead of getting the name from the rightmost column in this case the hundredths, as 0. This is an important idea that needs definite consolidation, so that students are very secure with it. It is related to understanding equivalent fractions. Top Expanded form: reunitising tenths, hundredths etc An idea central to dealing with the relative size of decimal numbers is to be able to interpret them in expanded form as decimals and as fractions.
This section demonstrates the challenge of the cognitive processing involved. A decimal such as 0. All these forms, except the last, can be obtained with a number expander. Condensed form 0. Exercise: Write down all the expanded and partially expanded forms that you can for: a 2.
To think of a number 0. Many children have difficulty deciding how or whether zeros change the value of a number. With decimals, children need to know that the zeros which affect the place value of the figures are on the left and the insignificant ones are on the right: 3.
Making 3. Using the ideas of expanded notation are crucial. The ones column must always be shown. Marked by decimal point, except in whole numbers. It is very hard for children who do not understand the place value basis of decimal numbers to memorize the rules.
Children generally decide which zeros change the value of a number according to their own interpretations of decimal notation. If a number has a decimal point , then the first digit to the right of the decimal point indicates the number of tenths. For example, the decimal 0. For example, the decimal 3. Note that the first digit to the left of the decimal point is the ones digit. You can write decimals with many places to the right of the decimal point.
For example, this is a representation of the mixed number 51 , with the place values named:. One good way to visualize decimals is by using base 10 blocks. For instance, suppose a large square respresents one whole.
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