La teoría de la elasticidad adaptativa de Cowin

In addition to mathematical equations, computer func- tions can also be included in the formulas. Functions are entered by (1) typing the functions, (2) selecting the

Formulas menu tab, selecting the function category from

the Function Library group, and selecting the function from the popup menu, or (3) by clicking on the Insert

Function button (shown in Figure 3-69) on the formula

bar to bring up the Insert Function dialogue box (shown in Figure 3-70). This section covers the rounding functions (including the CEILING and FLOOR functions), the SUM function, the AVERAGE function, and the IF function. Additional functions are available from the Insert Function dialogue box.

From the Function dialogue box the user may make a function available for selection by selecting All or the func- tion’s category from the Or select a category: dropdown box. Alternatively, the user may perform a key word search by typing key words in the Search for a function: text box and clicking on the Go button. When the function is shown in the Select a function: list box, the user double clicks on the function or selects the function and clicks on the OK button to bring up the Function Arguments dialogue box. The Function Arguments dialogue box for the ROUND function is shown in Figure 3-71. Each function has its own Function Arguments dialogue box.

The Function Arguments dialogue box prompts the user for the information necessary to complete the function. The user enters the requested information and clicks the OK button to close the Function Arguments dialogue box and create the function.

FIGURE 3-69 Insert Function Button

FIGURE 3-68 Spreadsheet for Exercise 3-6

FIGURE 3-71 Function Arguments Dialogue Box for the ROUND Function

Rounding

Excel provides the user three standard rounding func- tions: (1) ROUND, which rounds to the closest number; (2) ROUNDDOWN, which rounds the number down; and (3) ROUNDUP, which rounds the number up. Each of these functions requires the user to indicate the number or cell containing the number to be rounded (Number) and the number of digits to round to (Num_digits), in the following format:

=ROUND(<Number>,<Num_digits>)

The user does not need to capitalize the word “round” be- cause Excel will automatically capitalize the word “round” when the formula is completed. Rounding to a positive num- ber of digits represents the number of digits on the right side of the decimal point. For example, if the number of digits equals 2, the function rounds to hundredths. The function

=ROUND(123.228,2)

rounds 123.228 to 123.23. Figure 3-71 shows how this func- tion would be set up using the Function Arguments dialogue box for the ROUND function. Rounding to a negative num- ber of digits represents the number of digits on the left side of the decimal point. The function

=ROUND(123.228,-2)

rounds 123.228 to 100.00. The ROUNDUP function always rounds the number up and the ROUNDDOWN function al- ways rounds the number down. The function

=ROUNDUP(123.228,2)

rounds 123.228 up to 123.23, whereas the function =ROUNDDOWN(123.228,2)

rounds 123.228 down to 123.22.

The three standard rounding functions can only be used to round to decimal places, such as the hundreds, tens, whole numbers, tenths, hundredths, and so forth. The rounding

functions will not round to quarters of a yard. For this we must use the CEILING or FLOOR functions.

Ceiling

The CEILING function may be used to round up a number to the next multiple of a specified number (referred to by Excel as significance). For example, if the significance is 0.25, the CEILING function will round up to the next 0.25 incre- ment. The CEILING function requires the user to indicate the number or cell containing the number to be rounded (Number) and the significance, in the following format:

=CEILING(<Number>,<significance>)

For example, the function =CEILING(123.228,0.25)

rounds 123.228 to 123.25. Figure 3-72 shows how this func- tion would be set up using the Function Arguments dialogue box for the CEILING function.

Floor

The FLOOR function works in the same way as the CEILING function except it rounds down. For example, the function

=FLOOR(123.228,0.25)

rounds 123.228 to 123.00.

EXCEL QUICK TIP 3-4 Rounding to Nearest Quarter Yards

Excel’s rounding, CEILING, and FLOOR functions do not allow the user to automatically round to the nearest quarter-cubic-yards because Excel’s rounding functions will only round to decimal places (such as hundredths, tenths, tens, hundreds, and whole numbers) and the CEILING and FLOOR functions only round up or down,

FIGURE 3-72 Function Arguments Dialogue Box for the CEILING Function

not to the nearest quarter-cubic-yard. However, the user can round to the nearest quarter-cubic-yards by convert- ing the units to quarter-cubic-yards, rounding the num- ber to a whole number, and converting back to cubic yards. The formula for rounding a number in cubic yards to the nearest quarter-cubic-yard is written as follows:

=ROUND(<Number>*4,0)/4

For example, the following function is used to round 123.228 cubic yards to the nearest quarter-cubic-yard:

=ROUND(123.228*4,0)/4

The function first multiplies 123.228 cubic yards by 4 to get 492.912 quarter-cubic-yards, rounds 492.912 quarter- cubic-yards to 493 quarter-cubic-yards (the nearest whole number), and then divides 493 quarter-cubic-yards by 4 to get 123.25 cubic yards. Formulas can be written for other fractions of a whole number by using the same concepts.

Sum

The SUM function adds a group of numbers. It is particu- larly useful when adding a column, row, or block numbers, inasmuch as only the cells containing the first and last num- ber need to be included in the formula. The SUM function is written as follows:

=SUM(<Beginning Cell>:<Ending Cell>)

In Excel, the formula =SUM(C1:C5)

adds the numbers in Cells C1, C2, C3, C4, and C5. Noncontiguous cells may be added by placing a comma be- tween the cells references. The formula

=SUM(C1:C5,D17)

adds the numbers in Cells C1, C2, C3, C4, C5, and D17. The SUM function is quickly inserted into a cell by clicking on the

Formula menu tab and clicking on the AutoSum button in

the Function Library group. The AutoSum button is shown in Figure 3-73. The AutoSum will place a moving dashed line around the cells that Excel thinks the user wants to sum. If the user wants to include different cells, the user must select the cells. The AutoSum is completed by pressing the Enter key.