Intro to place value: FAQ

Place value is a key concept in understanding how numbers work. Without it, we wouldn't be able to tell the difference between, $100$100 and $10$10. We also use place value when we're adding, subtracting, multiplying, and dividing numbers, so it's important for all kinds of math!

Understanding place value is important in all kinds of math, from counting money to telling time to measuring things. Being able to compare numbers is also essential in many situations, like when we're trying to figure out which team won a game or who has the highest score.

Standard form is just the way we usually write numbers, like $567$567. Word form spells out the number in words, like "five hundred sixty-seven". Expanded form breaks the number down into its component parts, like $500+60+7$500, plus, 60, plus, 7.

Regrouping is when we exchange ten of one kind of unit for one of the next unit. For example, we can regroup ten ones into one ten, or ten tens into one hundred.

For example, we can regroup $\purpleD{50}\text{ tens}$start color #7854ab, 50, end color #7854ab, start text, space, t, e, n, s, end text into $\purpleD5\text{ hundreds}$start color #7854ab, 5, end color #7854ab, start text, space, h, u, n, d, r, e, d, s, end text.

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An $\blueE{\text{even}}$start color #0c7f99, start text, e, v, e, n, end text, end color #0c7f99 number is a number that can be split into $2$2 equal groups.

We find $\blueE{\text{even}}$start color #0c7f99, start text, e, v, e, n, end text, end color #0c7f99 numbers by making sure every object in the group has a pair.

Examples of $\blueE{\text{even}}$start color #0c7f99, start text, e, v, e, n, end text, end color #0c7f99 numbers are $\blueE2, \blueE4,\blueE6, \blueE8, \blueE{10}, . . .$start color #0c7f99, 2, end color #0c7f99, comma, start color #0c7f99, 4, end color #0c7f99, comma, start color #0c7f99, 6, end color #0c7f99, comma, start color #0c7f99, 8, end color #0c7f99, comma, start color #0c7f99, 10, end color #0c7f99, comma, point, point, point

An $\maroonE{\text{odd}}$start color #9e034e, start text, o, d, d, end text, end color #9e034e number cannot be split into $2$2 equal groups.

We find $\maroonE{\text{odd}}$start color #9e034e, start text, o, d, d, end text, end color #9e034e numbers by trying to pair objects and finding there is not always a pair.

Examples of $\maroonE{\text{odd}}$start color #9e034e, start text, o, d, d, end text, end color #9e034e numbers are $\maroonE1, \maroonE3, \maroonE5, \maroonE7, \maroonE9, . . .$start color #9e034e, 1, end color #9e034e, comma, start color #9e034e, 3, end color #9e034e, comma, start color #9e034e, 5, end color #9e034e, comma, start color #9e034e, 7, end color #9e034e, comma, start color #9e034e, 9, end color #9e034e, comma, point, point, point

We usually start by looking at the leftmost digit. If one number has a larger digit there, it's bigger. If the digits are the same, we move on to the next digit and compare those. If the numbers are the same all the way through, they're equal!