DECIMAL AND SEXAGESIMAL NUMBERS 3

You already know that the sexagesimal numeral system is used to measure time and angles.

Here we look at some processes that we should bear in mind when working with these magnitudes.

When expressing results

Also…

To get the result directly in the sexagesimal system:

4

We multiply the remainder of the hours (14) by 60 and continue dividing to get the minutes.

To solve a problem whose solution is an amount of time, we do the operations in the decimal system. However, the solution has to be given in traditional units of time, in other words, in the sexagesimal system.

Example

A cyclist covers the 49 kilometres of a time trial at an average speed of 35 km/h. What was the cyclist’s time?

Distance (km) : Speed (km/h) = Time (h)

The solution, one and four tenths of an hour, must be expressed in the sexagesimal system (hours and minutes).

To convert 0.4 hours into minutes, we multiply it by 60:

When entering the data in a problem

Also… 24 minutes are 60 24 of an hour: h = 24 : 60 = 0.4 h

When we are solving a problem, the data we use must be compatible, that is, expressed in the same units. This means that we sometimes have to convert quantities from the sexagesimal to the decimal system. Example

A cyclist covers the 49 kilometres of a time trial in one hour and twenty-four minutes. What was the cyclist’s average speed in km/h?

Distance (km) : Time (h) = Speed (km/h)

For the data to be compatible we have to express the time in hours.

To convert 24 minutes into hours, we divide it by 60:

1 h 24 min = (1 + 24 : 60) h = (1 + 0.4) h = 1.4 h

We calculate the speed: anayaeducacion.es

Remember conversions with units of time.

Let's practise!

1 A tap fills an 80-litre tank in 3 minutes and 12 seconds. How many litres does the tap supply per second?

2 A tap supplies 25 litres per minute. How long will it take to fill an 80-litre tank?

3 A shopping centre plays a music recording that lasts 5 minutes and 15 seconds on a loop for 7 hours. How many times does the recording play during this time?

Convert the data into minutes.

The Square Root Of A Decimal Number 4

You already know that calculating the square root is the opposite of squaring.

How to calculate the length of the side of a square given its area:

025 = 0.5

0.52 = 0.25

= 1.2 ï 1.22 = 1.44

You also know that there are many numbers which do not have an exact root. In such cases, we can approximate to as many decimal places as we want. As an example, we will calculate successive approximations of . 72 .

Algorithm for calculating square roots

We calculate the square root of a decimal using the same method that we use to calculate the square root of a natural number. From the decimal point, we lower the decimal places in twos, adding zeros until we get to the desired approximation.

Square roots using a calculator

Normally, to calculate the square root we use a calculator ($ key), which gives us the solution with many decimal places. We then round off that solution to as many decimal places as we need.

Let's practise! anayaeducacion.es Calculate and round off the roots of decimal numbers.

1 Calculate the following exact roots: a) 004 b) 049 c) 081 d) 0 0001 e) 0 0121 f ) 0 1125 a) 8 b) 11.5 c) 150 a) 784 b) 56 c) 39 0625 a) 10 b) 254 c) 76 38

2 Find the solution to one decimal place using trial and error.

3 Calculate on paper using the algorithm. If the result is not exact, find the solution to two decimal places.

4 Using a calculator, round off to the nearest thousandths.