System place value (Level 5)
When a student has a system place value understanding, he or she appreciates that the place value system (as powers of ten) can be extended indefinitely to the left and right of the decimal point. A student with an understanding of the system of place value recognizes that you can make a number as large as you like or as small as you like by repeatedly multiplying (or dividing) by 10. There is also a multi-unit awareness of the positional value of digits in a numeral and students can explain what happens when a number is multiplied or divided by a given power of ten. He or she knows that 0.003 times 1000 is 3 = 3.0 and that 300 x 200 = 60 000.
System place value is required for an understanding of multiplication and division of decimals by decimals. Students at this level also appreciate the relationship between values of adjacent places (units) in a numeral as well as the nature of repeating decimals. With repeating decimals a student needs to recognize that a decimal can go on forever because the place value system allows it.