Question

Change the following fractions to decimals. Carry division three decimal places as necessary. \(\frac{3}{50}\) ______

Short answer

0.06

Step-by-step solution

Understand the Fraction

The fraction given is \(\frac{3}{50}\). This fraction represents the division of 3 by 50 and needs to be converted to a decimal.

Set up the Division

To find the decimal, set up the division of 3 by 50. This means calculating 3 ÷ 50.

Perform the Division

Divide 3 by 50 using long division. Since 3 is less than 50, 0 whole units fit into 3 for the first decimal slot. Place a decimal point after 0 and continue the division by extending it three decimal places if necessary.

Calculate Further Decimals

Now, extend the decimal by adding zeroes to 3 (making it 3.000) and divide. - 3.0 ÷ 50 = 0.060 - Carry out: 30 ÷ 50 = 0 (remainder 30), - 300 ÷ 50 = 6 - Therefore, \(\frac{3}{50} = 0.060\) or simply 0.06 when rounded.

Review and Round If Necessary

Since the division as completed gives us 0.060, rounding is not necessary for three decimal places. The final decimal equivalent of \(\frac{3}{50}\) is 0.060, which simplifies to 0.06.

Key concepts

Long Division

Long division is a methodical process that helps us divide one number by another. It is particularly useful when the divisor is a large number, or when converting fractions to decimals, like in our case with \(\frac{3}{50}\). Begin by setting up the division with 3 as the dividend and 50 as the divisor. Since 3 is less than 50, it doesn’t fit, so we start off with 0 and place a decimal point immediately after.
Next, treat 3 as 3.000 by adding zeroes, enabling us to work through the long division process and get further into our calculated decimal. Each step asks us to multiply and subtract, gradually building smaller remainders until we achieve our precise result. It’s like slicing the number ever smaller until the decimal is revealed fully. Long division allows for calculations with great accuracy, crucial when we need a detailed decimal output.

Decimal Places

Decimals show portions of a whole number, which are very useful in precision. Decimal places refer to the digits that appear after the decimal point. The number of decimal places can affect the accuracy of a calculation.
In the example of converting \(\frac{3}{50}\), we aim to carry our division to three decimal places, i.e., calculating beyond the integer part to the third position to the right of the decimal. Here, the three decimal places are represented through the numbers 0.060.

• The hundredths place: 6
• The tenths place: 0
• The thousandths place: 0

Keep an eye on these positions, as this will ensure that the conversion process provides precision necessary for your application. Utilizing multiple decimal places typically improves accuracy.

Fraction Understanding

Fractions like \(\frac{3}{50}\) express parts of a whole as a ratio of numbers. The number on top is the numerator (3 in our case), and the number below is the denominator (50 here) this indicates how many pieces make up a whole.
Understanding judgments of size is important when comparing fractions or turning them into decimals. Realize that the numerator divided by the denominator gives insight into its scale. Smaller numerators with larger denominators provide smaller pieces, or if divided properly, smaller decimals. Thus, \(\frac{3}{50}\) tells us that our decimal will occupy very few whole parts, showing up as something less than 1.

Rounding Decimals

Rounding decimals involves adjusting the number to a nearby preferred decimal place, making it easier to read and interpret. This adjustment is straightforward when working with long decimal results. You simply look at the number in the decimal place immediately following your cutoff point and decide if the rounding should go up or remain the same.
In our example \(0.060\), since we carry only to three decimal places, and the result exactly reaches that removable simplification to \(0.06\) without compromising accuracy—no extra rounding is necessary here. Generally speaking, rounding rules stipulate round-up to the next higher digit if the cutoff digit is 5 or greater.

• 4 or lower stays the same
• 5 or higher rounds up

This practice of rounding is key when we wish to simplify yet keep the number close to its true value.