Dividing Decimals: 4.68 ÷ 0.003 Explained

by Natalie Brooks 42 views

Hey guys! Ever get stumped by decimal division? It can seem tricky at first, but breaking it down step-by-step makes it totally manageable. Today, we're going to tackle the problem of dividing 4.68 by 0.003. We'll walk through the process together, so you'll not only get the answer but also understand why it works. So, grab your pencils and let's get started!

Understanding Decimal Division

Before we dive into our specific problem, let's quickly refresh what decimal division is all about. Essentially, we're trying to figure out how many times the divisor (0.003 in our case) fits into the dividend (4.68). Think of it like this: if you have 4.68 candies and want to divide them into groups of 0.003 candies each, how many groups would you have? That's what division tells us!

The key to conquering decimal division lies in transforming the problem into one with whole numbers. Why? Because whole number division is something we're usually more comfortable with. So, how do we do this magical transformation? We use the power of multiplication!

The Trick: Multiplying by Powers of 10

The secret weapon in decimal division is multiplying both the divisor and the dividend by the same power of 10. This doesn't change the answer to the problem because it's like multiplying the entire equation by 1 (since multiplying by 10/10, 100/100, or 1000/1000 is the same as multiplying by 1). However, it allows us to shift the decimal point and turn our decimals into whole numbers.

To figure out which power of 10 to use, we look at the divisor. We want to multiply it by a power of 10 that will make it a whole number. In our problem (4.68 ÷ 0.003), the divisor is 0.003. It has three decimal places (the digits after the decimal point). To get rid of those decimals, we need to multiply by 1000 (which has three zeros).

So, remember this golden rule: identify the divisor, count its decimal places, and multiply both the divisor and the dividend by 10 raised to that power (10, 100, 1000, etc.).

Step-by-Step Solution: 4.68 ÷ 0.003

Okay, let's put our knowledge into action and solve 4.68 ÷ 0.003. We'll break it down into clear steps:

Step 1: Identify the Divisor and Dividend

First things first, let's pinpoint our players:

  • Dividend: 4.68 (the number being divided)
  • Divisor: 0.003 (the number we're dividing by)

Step 2: Determine the Power of 10

As we discussed, we need to transform our divisor (0.003) into a whole number. It has three decimal places, so we'll multiply both the divisor and the dividend by 1000:

Step 3: Multiply Both Numbers by 1000

Now, let's perform the multiplication:

    1. 68 * 1000 = 4680
    1. 003 * 1000 = 3

See the magic? Our problem has now transformed into a much friendlier one: 4680 ÷ 3.

Step 4: Perform the Division

Time for the main event! We'll use long division to divide 4680 by 3.

  1. Set up the long division:
    ____
3 | 4680
  1. Divide the first digit (4) by 3:
  • 3 goes into 4 once (1 * 3 = 3).
  • Write the '1' above the 4.
  • Subtract 3 from 4, leaving 1.
    1___
3 | 4680
    3
    ---
    1
  1. Bring down the next digit (6):
    1___
3 | 4680
    3
    ---
    16
  1. Divide 16 by 3:
  • 3 goes into 16 five times (5 * 3 = 15).
  • Write the '5' above the 6.
  • Subtract 15 from 16, leaving 1.
    15__
3 | 4680
    3
    ---
    16
    15
    ---
     1
  1. Bring down the next digit (8):
    15__
3 | 4680
    3
    ---
    16
    15
    ---
     18
  1. Divide 18 by 3:
  • 3 goes into 18 six times (6 * 3 = 18).
  • Write the '6' above the 8.
  • Subtract 18 from 18, leaving 0.
    156_
3 | 4680
    3
    ---
    16
    15
    ---
     18
     18
     ---
      0
  1. Bring down the last digit (0):
    156_
3 | 4680
    3
    ---
    16
    15
    ---
     18
     18
     ---
      00
  1. Divide 0 by 3:
  • 3 goes into 0 zero times (0 * 3 = 0).
  • Write the '0' above the 0.
  • Subtract 0 from 0, leaving 0.
    1560
3 | 4680
    3
    ---
    16
    15
    ---
     18
     18
     ---
      00
      0
      --
      0

Step 5: The Answer!

The result of our long division is 1560. So, 4.68 ÷ 0.003 = 1560.

Why This Works: A Deeper Dive

Now that we've got the answer, let's take a moment to understand why multiplying by powers of 10 works. Think of it in terms of fractions:

  1. 68 ÷ 0.003 is the same as 4.68 / 0.003

When we multiply both the numerator (4.68) and the denominator (0.003) by 1000, we're essentially multiplying the entire fraction by 1000/1000, which equals 1. Multiplying by 1 doesn't change the value of the fraction, but it does change how it looks:

(4.68 * 1000) / (0.003 * 1000) = 4680 / 3

So, we've transformed our decimal division problem into an equivalent whole number division problem. This makes the calculation much easier to manage.

Practice Makes Perfect

The best way to master decimal division is to practice! Try these problems on your own:

    1. 5 ÷ 0.5
    1. 96 ÷ 0.12
    1. 084 ÷ 0.007

Remember the steps: identify the divisor and dividend, find the right power of 10, multiply, and then divide. You'll be a decimal division pro in no time!

Common Mistakes to Avoid

While decimal division is straightforward once you get the hang of it, here are a few common mistakes to watch out for:

  • Forgetting to multiply both the divisor and the dividend: This is crucial! You need to maintain the balance of the equation.
  • Miscounting decimal places: Double-check that you're using the correct power of 10. A small error here can throw off your entire answer.
  • Rushing through long division: Take your time and be careful with each step. It's easy to make a mistake if you're rushing.
  • Not checking your answer: If you have time, multiply your answer by the original divisor. It should equal the original dividend. This is a great way to catch any errors.

Real-World Applications of Decimal Division

You might be wondering,