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Represent the same money amount in different ways

A learner understands that one monetary amount can be represented equivalently with different combinations of dollars, quarters, dimes, nickels, and pennies, or as cents and decimal dollars to the hundredths place. This reasoning relies on the equivalence of 100 cents and 1 dollar and on place value, including that the digits after the decimal represent tenths and hundredths of a dollar, not separate whole numbers; it does not extend to thousandths, rates, or algebraic generalizations.

Detailed Explanation: Represent the same money amount in different ways

The same money amount can be shown with coins, cents, or decimal dollars. Remember:

  • (100)(100) cents equals 11 dollar.
  • The first digit after the decimal shows tenths, or dimes.
  • The second digit shows hundredths, or cents.

Example: Represent 11 dollar and (37)(37) cents in different ways.

  1. Write it as decimal dollars:

    11 dollar and (37)(37) cents is 1.37$.

  2. Write it as cents:

    Since 11 dollar equals (100)(100) cents,

100+37=137 100+37=137

So the amount is (137)(137) cents.

  1. Show it with coins:

    One possible combination is:

1 dollar coin+1 quarter+1 dime+2 pennies 1\text{ dollar coin}+1\text{ quarter}+1\text{ dime}+2\text{ pennies}

Its value is

100+25+10+2=137 cents. 100+25+10+2=137\text{ cents}.

So these all represent the same amount:

$1.37=137 cents=1 dollar+1 quarter+1 dime+2 pennies\boxed{\$1.37=137\text{ cents}=1\text{ dollar}+1\text{ quarter}+1\text{ dime}+2\text{ pennies}}

Learn by doing: Represent the same money amount in different ways

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    Coin Math - Dollar Equivalent - Which Coins Equal a Dollar (Piles)

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