- Divide 590 by 10 to find that \(590 = \boxed{59 \text{ tens}}\).
- Divide 2,700 by 27 to find that \(2,700 = \boxed{27 \text{ hundreds}}\).
- Divide 63,000 by 63 to find that \(63,000 = \boxed{63 \text{ thousands}}\).
- Divide 480,000 by 10,000 to find that \(480,000 = \boxed{48 \text{ ten thousands}}\).
Explanation
- Place Value Analysis and Conversion Calculations
To determine the correct values, we use the principles of place value and base-10 numeration. Each conversion requires us to identify either the multiplier (how many of a unit make the number) or the unit itself (the place value representation) by performing division or division by powers of 10.
- For the first equation, \(590 = \text{____ tens}\), we need to determine how many groups of 10 fit into 590. This is calculated as \(590 \div 10 = 59\).
- For the second equation, \(2,700 = 27 \text{ ____}\), we need to determine which unit 27 must be multiplied by to equal 2,700. We calculate \(2,700 \div 27 = 100\). Since 100 represents the "hundreds" place, the missing word is "hundreds".
- For the third equation, \(63,000 = 63 \text{ ____}\), we perform a similar operation: \(63,000 \div 63 = 1,000\). Since 1,000 represents the "thousands" place, the missing word is "thousands".
- For the fourth equation, \(480,000 = \text{____ ten thousands}\), we need to determine how many groups of 10,000 fit into 480,000. This is calculated as \(480,000 \div 10,000 = 48\).
- Final Results
Based on the calculations above, we can now list the completed equations:
- \(590 = 59 \text{ tens}\)
- \(2,700 = 27 \text{ hundreds}\)
- \(63,000 = 63 \text{ thousands}\)
- \(480,000 = 48 \text{ ten thousands}\)
Examples
Regrouping is essential in everyday life, such as in finance when dealing with different denominations of currency. For instance, if you have \$590 and want to know how many 10-dollar bills you would need, you perform the division \(590 \div 10 = 59\). Similarly, when managing large inventories or savings, converting totals into larger units like hundreds, thousands, or ten thousands helps simplify record-keeping and mental calculations. Understanding these place value shifts is a foundational skill for managing larger quantities effectively.