84/ 0.7= _

To solve \(\frac { 84} { 0.7} \):
Convert 0.7 to a fraction:
\[0.7 = \frac { 7} { 10} \]
So the division becomes:
\[\frac { 84} { 0.7} = 84 \div 0.7\]
Rewrite the division as multiplication by the reciprocal:
\[84 \div 0.7 = 84 \times \frac { 10} { 7} \]
Simplify the multiplication:
\[84 \times \frac { 10} { 7} = \frac { 84 \times 10} { 7} = \frac { 840} { 7} = 120\]
Thus:
\[\frac { 84} { 0.7} = 120\]

Supplemental Knowledge

When dividing by decimals, simplifying division can be done by multiplying both numerator (which you are dividing by) and denominator by their respective powers of 10 until both end up as whole numbers.
For example, dividing 84 by 0.7 can be transformed as follows:

1. Multiply both 84 and 0.7 by 10 to eliminate the decimal in the denominator.
2. This changes the problem to \(840 \div 7\).
   Now, you can perform simple division.

Real-World Applications

Imagine you are at a store and want to buy items priced at 0.70 dollars each, and you have 84 dollars. To find out how many items you can buy, you'd perform this division:

• By converting 0.70 dollars to cents (70 cents), you change your calculation from dollars to cents.
• Similarly, converting 84 dollars to cents gives you 8400 cents.
• Dividing these values (8400 ÷ 70) will tell you how many items you can purchase.
  This practical application helps in budgeting and understanding how unit prices affect your total spending.

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